Question

Which of the following can not be the direction cosines of a line?

Options

• `sqrt(1/5), - sqrt(1/2), sqrt(3/10)`

• `1/sqrt3, (- 1)/sqrt3, 1/sqrt3`

• `1/sqrt2, (- 1)/sqrt2, (- 1)/sqrt2`

• `1/sqrt2, (-1)/sqrt2, 0`

Answer 1

`1/sqrt2, (- 1)/sqrt2, (- 1)/sqrt2`

Explanation:

We know that, l² + m² + n² = 1

Since, `(1/sqrt2)^2 + ((- 1)/sqrt2)^2 + ((- 1)/sqrt2)^2`

`= 1/2 + 1/2 + 1/2`

`= 3/2 ne 1`