Question

If a = `3hati - 2hatj + hatk` and b = `2hati - 4hatj - 3hatk`, then | a – 2b | will be ______.

Options

• 9

• `sqrt(86)`

• `sqrt(94)`

• 10

Answer 1

If a = `3hati - 2hatj + hatk` and b = `2hati - 4hatj - 3hatk`, then | a – 2b | will be `underlinebb(sqrt(86))`.

Explanation:

a = `3hati - 2hatj + hatk`    ...(i)

b = `2hati - 4hatj - 3hatk`    ...(ii)

Multiplying by 2 on both sides, we get

2b = `4hati - 8hatj - 6hatk`  ...(iii)

Subtracting equation (iii) from equation (i), we get

a – 2b = `(3hati - 2hatj + hatk) - (4hati - 8hatj - 6hatk)`

= `-hati + 6hatj + 7hatk`

= `sqrt((-1)^2 + (6)^2 + (7)^2`

= `sqrt(86)`