Question

Unit vector along `vec(PQ)`, where coordinates of P and Q respectively are (2, 1, – 1) and (4, 4, – 7), is ______.

Options

• `2hati + 3hatj - 6hatk`

• `-2hati - 3hatj + 6hatk`

• `(-2hati)/7 - (3hatj)/7 + (6hatk)/7`

• `(2hati)/7 + (3hatj)/7 - (6hatk)/7`

Answer 1

Unit vector along `vec(PQ)`, where coordinates of P and Q respectively are (2, 1, – 1) and (4, 4, – 7), is `underlinebb((2hati)/7 + (3hatj)/7 - (6hatk)/7)`.

Explanation:

given:

• Point P(2, 1, −1)

• Point Q(4, 4, −7)

`vec(PQ) = vecQ-vecP=(4-2, 4-1,-7-(-1)) = (2, 3,-6)`

`vec(PQ) = 2hati + 3hatj - 6hatk`

`|vec(PQ)|=sqrt(2^2+3^2+(-6)^2) = sqrt(4+9+36)=sqrt49 = 7`

Unit vector `= vec(PQ)/|vec(PQ)| = 1/7(2hati+3hatj-6hatk)`

`=(2hati)/7 + (3hatj)/7 - (6hatk)/7`