Question

What will be projection of the vector `4hati - 3hatj + hatk` on the line joining the points (2, 3, – 1) and (– 2, – 4, 3)?

Options

• 1

• 2

• 3

• 4

Answer 1

1

Explanation:

Let point A = (2, 3, – 1) and point B = (–2, –4, 3).

Now the position vector of line joining A and B,

AB = OB = OA = `2hati - 4hatj + 3hatk - 2hati - 3hatj + hatk`

= `-4hati - 7hatj + 4hatk`

Again let a = AB = `-4hati - 7hatj + 4hatk`

and b = `4hati - 3hatj + hatk`

Then, a.b = `(-4hati - 7hatj + 4hatk).(4hati - 3hatj + hatk)`

= – 16 + 21 + 4

= 9

| a | = `sqrt((-4)^2 + (-7)^2 + (4)^2`

= `sqrt(16 + 49 + 16)`

= 9

Now projection of b on a

= `((a.b))/|a|`

= `9/9`

= 1