Question

If A- 2i-3j+k and B-3i+j-2k, then the cosine of the angle between the two vectors is?​

Answer 1

Here is your answer. Hope it helps...

Answer 2

Given,

Two vectors A = 2i-3j+k and B = 3i+j-2k.

To Find,

The cosine of the angle between the two vectors.

Solution,

We will use the formula of the dot product to find the cosine of the angle between the two vectors.

a.b = |a||b| cosθ

Now,

a.b = (2i-3j+k).(3i+j-2k)

a.b = 2(3)-3(1)-(2)

a.b = 6-3-2 = 1

|a| = √(2²+3²+1²) = √14

|b| = √(3²+1²+2²) = √14

cos θ = a.b/|a||b|

cos θ = 1/√14√14 = 1/14

Hence, the cosine of the angle between the two vectors is 1/14.