Finding Components of Vectors - Pre-Calculus
Card 1 of 30
What is the component form of the vector from $P(-4,6)$ to $Q(1,-2)$?
What is the component form of the vector from $P(-4,6)$ to $Q(1,-2)$?
Tap to reveal answer
$\langle 5,,-8\rangle$. Calculate: $\langle 1-(-4), -2-6\rangle = \langle 5, -8\rangle$.
$\langle 5,,-8\rangle$. Calculate: $\langle 1-(-4), -2-6\rangle = \langle 5, -8\rangle$.
← Didn't Know|Knew It →
What is the component form of the vector from $P(2,-1)$ to $Q(7,3)$?
What is the component form of the vector from $P(2,-1)$ to $Q(7,3)$?
Tap to reveal answer
$\langle 5,,4\rangle$. Calculate: $\langle 7-2, 3-(-1)\rangle = \langle 5, 4\rangle$.
$\langle 5,,4\rangle$. Calculate: $\langle 7-2, 3-(-1)\rangle = \langle 5, 4\rangle$.
← Didn't Know|Knew It →
Identify the $y$-component of the vector from $P(x_1,y_1)$ to $Q(x_2,y_2)$.
Identify the $y$-component of the vector from $P(x_1,y_1)$ to $Q(x_2,y_2)$.
Tap to reveal answer
$y_2-y_1$. The vertical displacement from initial to terminal point.
$y_2-y_1$. The vertical displacement from initial to terminal point.
← Didn't Know|Knew It →
Identify the $x$-component of the vector from $P(x_1,y_1)$ to $Q(x_2,y_2)$.
Identify the $x$-component of the vector from $P(x_1,y_1)$ to $Q(x_2,y_2)$.
Tap to reveal answer
$x_2-x_1$. The horizontal displacement from initial to terminal point.
$x_2-x_1$. The horizontal displacement from initial to terminal point.
← Didn't Know|Knew It →
What operation produces vector components from initial $P(x_1,y_1)$ to terminal $Q(x_2,y_2)$?
What operation produces vector components from initial $P(x_1,y_1)$ to terminal $Q(x_2,y_2)$?
Tap to reveal answer
Subtract initial coordinates from terminal: $Q-P$. Vector components are found by terminal minus initial coordinates.
Subtract initial coordinates from terminal: $Q-P$. Vector components are found by terminal minus initial coordinates.
← Didn't Know|Knew It →
State the formula for the component form of the vector from $P(x_1,y_1)$ to $Q(x_2,y_2)$.
State the formula for the component form of the vector from $P(x_1,y_1)$ to $Q(x_2,y_2)$.
Tap to reveal answer
$\langle x_2-x_1,,y_2-y_1\rangle$. Terminal minus initial gives the displacement vector.
$\langle x_2-x_1,,y_2-y_1\rangle$. Terminal minus initial gives the displacement vector.
← Didn't Know|Knew It →
Identify the component form of the vector from $P(6,-3)$ to $Q(6,-9)$.
Identify the component form of the vector from $P(6,-3)$ to $Q(6,-9)$.
Tap to reveal answer
$\langle 0,,-6\rangle$. Calculate: $\langle 6-6, -9-(-3)\rangle = \langle 0, -6\rangle$.
$\langle 0,,-6\rangle$. Calculate: $\langle 6-6, -9-(-3)\rangle = \langle 0, -6\rangle$.
← Didn't Know|Knew It →
Identify the component form of the vector from $P(-3,1)$ to $Q(2,1)$.
Identify the component form of the vector from $P(-3,1)$ to $Q(2,1)$.
Tap to reveal answer
$\langle 5,,0\rangle$. Calculate: $\langle 2-(-3), 1-1\rangle = \langle 5, 0\rangle$.
$\langle 5,,0\rangle$. Calculate: $\langle 2-(-3), 1-1\rangle = \langle 5, 0\rangle$.
← Didn't Know|Knew It →
What is the component form of the vector from $P(a,b)$ to $Q(c,d)$?
What is the component form of the vector from $P(a,b)$ to $Q(c,d)$?
Tap to reveal answer
$\langle c-a,,d-b\rangle$. General formula: terminal minus initial coordinates.
$\langle c-a,,d-b\rangle$. General formula: terminal minus initial coordinates.
← Didn't Know|Knew It →
What is $\overrightarrow{QP}$ in component form if $\overrightarrow{PQ}=\langle 7,-2\rangle$?
What is $\overrightarrow{QP}$ in component form if $\overrightarrow{PQ}=\langle 7,-2\rangle$?
Tap to reveal answer
$\langle -7,,2\rangle$. Reverse vector has opposite components: negate each component.
$\langle -7,,2\rangle$. Reverse vector has opposite components: negate each component.
← Didn't Know|Knew It →
Find and correct the error: $A(1,4)$, $B(6,0)$, claimed $\overrightarrow{AB}=\langle -5,4\rangle$.
Find and correct the error: $A(1,4)$, $B(6,0)$, claimed $\overrightarrow{AB}=\langle -5,4\rangle$.
Tap to reveal answer
Correct: $\overrightarrow{AB}=\langle 5,,-4\rangle$. Should be $\langle 6-1, 0-4\rangle = \langle 5, -4\rangle$, not negated.
Correct: $\overrightarrow{AB}=\langle 5,,-4\rangle$. Should be $\langle 6-1, 0-4\rangle = \langle 5, -4\rangle$, not negated.
← Didn't Know|Knew It →
Which option is the correct component form for $\overrightarrow{AB}$ if $A(-1,2)$ and $B(3,-5)$?
Which option is the correct component form for $\overrightarrow{AB}$ if $A(-1,2)$ and $B(3,-5)$?
Tap to reveal answer
$\langle 4,,-7\rangle$. Calculate: $\langle 3-(-1), -5-2\rangle = \langle 4, -7\rangle$.
$\langle 4,,-7\rangle$. Calculate: $\langle 3-(-1), -5-2\rangle = \langle 4, -7\rangle$.
← Didn't Know|Knew It →
Find the initial point $P$ if $Q(5,-4)$ and $\overrightarrow{PQ}=\langle 2,3\rangle$.
Find the initial point $P$ if $Q(5,-4)$ and $\overrightarrow{PQ}=\langle 2,3\rangle$.
Tap to reveal answer
$P(3,-7)$. Subtract vector from terminal: $(5,-4) - \langle 2,3\rangle = (3,-7)$.
$P(3,-7)$. Subtract vector from terminal: $(5,-4) - \langle 2,3\rangle = (3,-7)$.
← Didn't Know|Knew It →
Find the terminal point $Q$ if $P(2,3)$ and $\overrightarrow{PQ}=\langle 4,-1\rangle$.
Find the terminal point $Q$ if $P(2,3)$ and $\overrightarrow{PQ}=\langle 4,-1\rangle$.
Tap to reveal answer
$Q(6,2)$. Add vector to initial point: $(2,3) + \langle 4,-1\rangle = (6,2)$.
$Q(6,2)$. Add vector to initial point: $(2,3) + \langle 4,-1\rangle = (6,2)$.
← Didn't Know|Knew It →
What is the component form of the vector from $P(1.5,-2)$ to $Q(4.5,1)$?
What is the component form of the vector from $P(1.5,-2)$ to $Q(4.5,1)$?
Tap to reveal answer
$\langle 3,,3\rangle$. Calculate: $\langle 4.5-1.5, 1-(-2)\rangle = \langle 3, 3\rangle$.
$\langle 3,,3\rangle$. Calculate: $\langle 4.5-1.5, 1-(-2)\rangle = \langle 3, 3\rangle$.
← Didn't Know|Knew It →
What is the component form of the vector from $P(-5,4)$ to $Q(-9,10)$?
What is the component form of the vector from $P(-5,4)$ to $Q(-9,10)$?
Tap to reveal answer
$\langle -4,,6\rangle$. Calculate: $\langle -9-(-5), 10-4\rangle = \langle -4, 6\rangle$.
$\langle -4,,6\rangle$. Calculate: $\langle -9-(-5), 10-4\rangle = \langle -4, 6\rangle$.
← Didn't Know|Knew It →
What is the component form of the vector from $P(3,8)$ to $Q(-1,0)$?
What is the component form of the vector from $P(3,8)$ to $Q(-1,0)$?
Tap to reveal answer
$\langle -4,,-8\rangle$. Calculate: $\langle -1-3, 0-8\rangle = \langle -4, -8\rangle$.
$\langle -4,,-8\rangle$. Calculate: $\langle -1-3, 0-8\rangle = \langle -4, -8\rangle$.
← Didn't Know|Knew It →
What is the component form of the vector from $P(-2,-7)$ to $Q(-2,1)$?
What is the component form of the vector from $P(-2,-7)$ to $Q(-2,1)$?
Tap to reveal answer
$\langle 0,,8\rangle$. Calculate: $\langle -2-(-2), 1-(-7)\rangle = \langle 0, 8\rangle$.
$\langle 0,,8\rangle$. Calculate: $\langle -2-(-2), 1-(-7)\rangle = \langle 0, 8\rangle$.
← Didn't Know|Knew It →
What is the component form of the vector from $P(9,2)$ to $Q(4,2)$?
What is the component form of the vector from $P(9,2)$ to $Q(4,2)$?
Tap to reveal answer
$\langle -5,,0\rangle$. Calculate: $\langle 4-9, 2-2\rangle = \langle -5, 0\rangle$.
$\langle -5,,0\rangle$. Calculate: $\langle 4-9, 2-2\rangle = \langle -5, 0\rangle$.
← Didn't Know|Knew It →
What is the component form of the vector from $P(0,0)$ to $Q(-3,5)$?
What is the component form of the vector from $P(0,0)$ to $Q(-3,5)$?
Tap to reveal answer
$\langle -3,,5\rangle$. Calculate: $\langle -3-0, 5-0\rangle = \langle -3, 5\rangle$.
$\langle -3,,5\rangle$. Calculate: $\langle -3-0, 5-0\rangle = \langle -3, 5\rangle$.
← Didn't Know|Knew It →
Find $P$ if $Q(-1,6)$ and $\overrightarrow{PQ}=\langle 3,-2\rangle$.
Find $P$ if $Q(-1,6)$ and $\overrightarrow{PQ}=\langle 3,-2\rangle$.
Tap to reveal answer
$P(-4,8)$. Subtract vector from terminal: $P = (-1-3, 6-(-2))$.
$P(-4,8)$. Subtract vector from terminal: $P = (-1-3, 6-(-2))$.
← Didn't Know|Knew It →
What is the component form of the vector from $P(3,7)$ to $Q(-4,1)$?
What is the component form of the vector from $P(3,7)$ to $Q(-4,1)$?
Tap to reveal answer
$\langle -7,\ -6\rangle$. Calculate $\langle -4-3, 1-7\rangle = \langle -7, -6\rangle$.
$\langle -7,\ -6\rangle$. Calculate $\langle -4-3, 1-7\rangle = \langle -7, -6\rangle$.
← Didn't Know|Knew It →
What is the component form of the vector from $P(-6,0)$ to $Q(-1,-5)$?
What is the component form of the vector from $P(-6,0)$ to $Q(-1,-5)$?
Tap to reveal answer
$\langle 5,\ -5\rangle$. Calculate $\langle -1-(-6), -5-0\rangle = \langle 5, -5\rangle$.
$\langle 5,\ -5\rangle$. Calculate $\langle -1-(-6), -5-0\rangle = \langle 5, -5\rangle$.
← Didn't Know|Knew It →
What operation gives vector components from initial point $P$ to terminal point $Q$ in the plane?
What operation gives vector components from initial point $P$ to terminal point $Q$ in the plane?
Tap to reveal answer
Subtract coordinates: $Q-P$. Terminal coordinates minus initial coordinates gives components.
Subtract coordinates: $Q-P$. Terminal coordinates minus initial coordinates gives components.
← Didn't Know|Knew It →
What is the component form of the vector from $P(-4,6)$ to $Q(1,2)$?
What is the component form of the vector from $P(-4,6)$ to $Q(1,2)$?
Tap to reveal answer
$\langle 5,\ -4\rangle$. Calculate $\langle 1-(-4), 2-6\rangle = \langle 5, -4\rangle$.
$\langle 5,\ -4\rangle$. Calculate $\langle 1-(-4), 2-6\rangle = \langle 5, -4\rangle$.
← Didn't Know|Knew It →
What is the component form of the vector from $P(0,0)$ to $Q(-3,8)$?
What is the component form of the vector from $P(0,0)$ to $Q(-3,8)$?
Tap to reveal answer
$\langle -3,\ 8\rangle$. Calculate $\langle -3-0, 8-0\rangle = \langle -3, 8\rangle$.
$\langle -3,\ 8\rangle$. Calculate $\langle -3-0, 8-0\rangle = \langle -3, 8\rangle$.
← Didn't Know|Knew It →
What is the component form of the vector from $P(5,5)$ to $Q(5,-2)$?
What is the component form of the vector from $P(5,5)$ to $Q(5,-2)$?
Tap to reveal answer
$\langle 0,\ -7\rangle$. Calculate $\langle 5-5, -2-5\rangle = \langle 0, -7\rangle$.
$\langle 0,\ -7\rangle$. Calculate $\langle 5-5, -2-5\rangle = \langle 0, -7\rangle$.
← Didn't Know|Knew It →
What is the component form of the vector from $P(-2,-3)$ to $Q(-2,4)$?
What is the component form of the vector from $P(-2,-3)$ to $Q(-2,4)$?
Tap to reveal answer
$\langle 0,\ 7\rangle$. Calculate $\langle -2-(-2), 4-(-3)\rangle = \langle 0, 7\rangle$.
$\langle 0,\ 7\rangle$. Calculate $\langle -2-(-2), 4-(-3)\rangle = \langle 0, 7\rangle$.
← Didn't Know|Knew It →
What is the component form of the vector from $P(9,-1)$ to $Q(2,-1)$?
What is the component form of the vector from $P(9,-1)$ to $Q(2,-1)$?
Tap to reveal answer
$\langle -7,\ 0\rangle$. Calculate $\langle 2-9, -1-(-1)\rangle = \langle -7, 0\rangle$.
$\langle -7,\ 0\rangle$. Calculate $\langle 2-9, -1-(-1)\rangle = \langle -7, 0\rangle$.
← Didn't Know|Knew It →
What is the component form of the vector from $P(-10,4)$ to $Q(-3,12)$?
What is the component form of the vector from $P(-10,4)$ to $Q(-3,12)$?
Tap to reveal answer
$\langle 7,\ 8\rangle$. Calculate $\langle -3-(-10), 12-4\rangle = \langle 7, 8\rangle$.
$\langle 7,\ 8\rangle$. Calculate $\langle -3-(-10), 12-4\rangle = \langle 7, 8\rangle$.
← Didn't Know|Knew It →