Question

The angle between 6 ICAP + 3 j cap + 2 k cap and two ICAP - 2 j cap - k cap

Answer 1

Given,

First vector is = 6i+3j+2k

Second vector is = 2i-2j-k

To find,

The angle between the two vectors.

Solution,

We can simply solve this mathematical problem by using the following mathematical process.

Let,

First vector = a

Second vector = b

|a| = √(6)²+(3)²+(2)² = √(36+9+4) = √49 = 7

|b| = √(2)²+(-2)²+(-1)² = √(4+4+1) = √9 = 3

a.b = (6)×(2)+(3)×(-2)+(2)×(-1) = 12-6-2 = 4

Let, angle between two vectors = θ

Now,

cos θ = (a.b)/(|a| |b|)

cos θ = 4/(3×7)

cos θ = 4/21

θ = cos⁻¹ 4/21

θ = 79.02°

Hence, the angle between two vectors is 79.02°