Question

angle between vectors is equal to two ICAP + 2 J cap - 2 k cap and b is equals to 3 ICAP - 4 j cap is​

Answer 1

Answer: The angle between vectors A and B is 96.63 degrees.

Explanation:

It is given that,

Vector, A=2i+2j-2kA=2i+2j−2k

Vector, B=3i-4jB=3i−4j

We need to find the angle between A and B. It an be calculated using dot product formula such that,

A.B=|A||B|\ cos\thetaA.B=∣A∣∣B∣ cosθ

Magnitude of A, |A|=\sqrt{2^2+2^2+2^2} =3.464∣A∣=

2

2

+2

2

+2

2

​

=3.464

Magnitude of B, |B|=\sqrt{3^2+(-4)^2} =5∣B∣=

3

2

+(−4)

2

​

=5

Dot product of A and B, A.B=6-8+0=-2A.B=6−8+0=−2

cos\theta=\dfrac{A.B}{|A||B|}cosθ=

∣A∣∣B∣

A.B

​

cos\theta=\dfrac{-2}{3.464\times 5}cosθ=

3.464×5

−2

​

\theta=96.63^{\circ}θ=96.63

∘

So, the angle between vectors A and B is 96.63 degrees. Hence, this is the required solution.

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