Question

The direction cosines of the line passing through the points P(2, 3, 5) and Q(–1, 2, 4) are ______.

Options

• `(3/sqrt11, 1/sqrt11, 1/sqrt11)`

• `(1/sqrt11, 1/sqrt11, 1/sqrt11)`

• `(3/sqrt11, (−1)/sqrt11, (−1)/sqrt11)`

• `((−3)/sqrt11, 1/sqrt11, (−1)/sqrt11)`

Answer 1

The direction cosines of the line passing through the points P(2, 3, 5) and Q(–1, 2, 4) are `underlinebb(3/sqrt11, 1/sqrt11, 1/sqrt11)`.

Explanation:

The direction ratios (DRs) of the line PQ are obtained by subtracting the coordinates:

(−1 − 2, 2 − 3, 4 − 5)

= (−3, −1, −1)

To find direction cosines, divide the DRs by the magnitude

`sqrt((−3)^2 + (−1)^2 + (−1)^2)`

= `sqrt11`

Changing the sign (as direction can be taken from Q to P)