Question

Write a unit vector in the direction of the sum of vectors a = 2 i + 2 j - 5 k and vector b = 2i + j -7 k.

Answer 1

Solution:
The sum of the vector a & b is,
vect a + vect b = (2+2)i + (2+1)j + (-5-7)k
= 4i + 3j - 12k

Let (vect a + vect b) be called as vect c.
Now, unit vector in the direction of vect c is,
$unit \: vect \: of \: c \: = \: \frac{1}{ |vect \: c| } \times vect \: c$
|vect c| = √(4^2 + 3^2 - 12^2)
= √(16 + 9 + 144)
= √169
= 13

Therefore, unit vect of vect c
= (1/13) × 4i + (1/13) × 3j - (1/13) × 12k
= (4/13)i + (3/13)j - (12/13)k

Hope you got it!