Question

Given , vector A = 2i - j + 3k and vector B = 3i - 2j - 2k . Find the unit vector of (a) (A+B) (b) (A-B)

Answer 1

Answer

u = (5i -3j +k) / √35

u = (-i +j+5k) / 3√3 .

Explanation

1. To add or subtract two vectors, add or subtract the corresponding components.

2. Formula to find unit vector is u = →v / | →v |

| →v | = √(i² + j² + ²k)

a)

(A+B)

A = 2i - j + 3k

B = 3i - 2j - 2k

A+B = (2+3)i + (-1+-2)j + (3+(-2))k

A+B = D = 5i  - 3j + k

|D| = √5² + 3² +1²

|D| =√35

So the unit vector u = (5i -3j +k) / √35

b)

(A-B)

A = 2i - j + 3k

B = 3i - 2j - 2k

A-B = (2-3)i + (-1-(-2))j + (3-(-2))

A-B  = C = -i + j + 5k

|C| = √(1²+1²+5²)

|C| = 3√3

So the unit vector u = (-i +j+5k) / 3√3 .

Answer 2

Given , vector A = 2i - j + 3k and vector B = 3i - 2j - 2k . Find the unit vector of (a) (A+B) (b) (A-B)