Find the cosine of the angle between the two vectors $\langle 1,2 \rangle$ and $\langle - 2,1 \rangle$ .
A) $\frac { 1 } { \sqrt { 2 } }$
B)0
C) $\frac { 1 } { \sqrt { 3 } }$
D)1
E) $\frac { 1 } { \sqrt { 5 } }$
F) $\frac { 1 } { 2 }$
G) $\frac { 4 } { 3 }$
H) $\frac { 3 } { 4 }$

Question

Find the cosine of the angle between the two vectors $\langle 1,2 \rangle$ and $\langle - 2,1 \rangle$ .
A) $\frac { 1 } { \sqrt { 2 } }$ 
B)0
C) $\frac { 1 } { \sqrt { 3 } }$ 
D)1
E) $\frac { 1 } { \sqrt { 5 } }$ 
F) $\frac { 1 } { 2 }$ 
G) $\frac { 4 } { 3 }$ 
H) $\frac { 3 } { 4 }$

Quizplus · Accepted Answer

The dot product of the vectors $\langle 1,2 \rangle$ and $\langle -2,1 \rangle$ is $1(-2) + 2(1) = -2 + 2 = 0$. Since the dot product is zero, the vectors are orthogonal, and the cosine of the angle between them is 0.

Find the Cosine of the Angle Between the Two Vectors ⟨1,2⟩\langle 1,2 \rangle⟨1,2⟩

Find the Cosine of the Angle Between the Two Vectors $\langle 1,2 \rangle$