Solving Problems with Vectors and Velocity
Precalculus · Flashcards · Recall
PRECALCULUS · FLASHCARDS
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QUESTION
State the formula for the vector projection of
a
⃗
\vec{a}
a
onto a nonzero vector
b
⃗
\vec{b}
b
.
QUESTION
What is the unit vector in the direction of
v
⃗
\vec{v}
v
(assuming
v
⃗
≠
0
⃗
\vec{v}\neq\vec{0}
v
=
0
)?
QUESTION
What is the formula for the projection of
v
⃗
\vec{v}
v
onto
u
⃗
\vec{u}
u
(vector projection)?
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ANSWER
proj
u
⃗
v
⃗
=
v
⃗
⋅
u
⃗
∥
u
⃗
∥
2
u
⃗
\text{proj}_{\vec{u}}\vec{v}=\frac{\vec{v}\cdot\vec{u}}{\|\vec{u}\|^2}\,\vec{u}
proj
u
v
=
∥
u
∥
2
v
⋅
u
u
. Projects
v
⃗
\vec{v}
v
onto
u
⃗
\vec{u}
u
using dot product and scaling.
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