Vector Algebra · Question 38

If the components of a = i + j + k along and perpendicular to b = 3 i + j - k respectively, are 1611(3 i + j - k) and 111(-4 i - 5 j - 17 k), then 2 + 2 + 2 is equal to:

1. 16
2. 23
3. 26
4. 18

Answer

(3) 26

Solution

a = (component along b) + (component perpendicular to b)

a = 1611(3 i + j - k) + 111(-4 i - 5 j - 17 k)

= 111(44 i + 11 j - 33 k)

= 4 i + j - 3 k

= 4, = 1, = -3

(Check: a b| b|2 = 12 + 1 + 311 = 1611)

2 + 2 + 2 = 16 + 1 + 9 = 26

Answer: (3)