Question

5. Find the angles between the following pairs of
vectors :
(1) ả=i+ j+k and B = -2i-2j-2k​
no spam

Answer 1

Explanation:

we will use the method of dot product of vectors

A•B = |A| |B|cos $

..... where A and B are given vectors , $ is the angle between them and |A| and |B| are the magnitude of given vectors respectively.

now,

A • B = 1(-2) + 1(-2) + 1(-2) = -6

|A| = √(1²+1²+1²) = √3

|B| = √((-2)²+(-2)²+(-2)²) = ✓12 or 2√3

now,

A•B = |A| |B|cos $

-6 = √3 x 2√3 cos $

-6 = 2x 3 cos $

cos $ = -6/6 = -1

since, cos 180° = -1

therefore, $ =180°

or the angle between the given two vectors is 180°