Multivariable Calculus Quiz
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VECTORS AND GEOMETRY IN 3D
Question 1
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Consider vectors
p
=
⟨
1
,
2
,
−
1
⟩
\mathbf{p} = \langle 1, 2, -1 \rangle
p
=
⟨
1
,
2
,
−
1
⟩
and
q
=
⟨
3
,
−
1
,
2
⟩
\mathbf{q} = \langle 3, -1, 2 \rangle
q
=
⟨
3
,
−
1
,
2
⟩
. If the angle between
p
\mathbf{p}
p
and
r
\mathbf{r}
r
is
60
°
60°
60°
and the angle between
q
\mathbf{q}
q
and
r
\mathbf{r}
r
is
120
°
120°
120°
, where
∣
∣
r
∣
∣
=
2
||\mathbf{r}|| = 2
∣∣
r
∣∣
=
2
, what is
p
⋅
r
+
q
⋅
r
\mathbf{p} \cdot \mathbf{r} + \mathbf{q} \cdot \mathbf{r}
p
⋅
r
+
q
⋅
r
?
A
6
−
14
\sqrt{6} - \sqrt{14}
6
−
14
B
2
6
−
2
14
2\sqrt{6} - 2\sqrt{14}
2
6
−
2
14
C
14
−
6
\sqrt{14} - \sqrt{6}
14
−
6
D
2
14
−
2
6
2\sqrt{14} - 2\sqrt{6}
2
14
−
2
6
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