Question

If the distance of the point (1, 1, 1) from the origin is half its distance from the plane x + y + z + k = 0, then k = ______.

विकल्प

• ± 3

• ± 6

• –3, 6

• 3, – 9

Answer 1

If the distance of the point (1, 1, 1) from the origin is half its distance from the plane x + y + z + k = 0, then k = 3, – 9.

Explanation:

The distance of (1, 1, 1) from the origin is

d = `sqrt((1)^2 + (1)^2 + (1)^2) = sqrt(3)`

Distance of (1, 1, 1) from x + y + z + k = 0 is

`"d"_1 = |((1) + (1) + (1) + "k")/sqrt((1)^2 + (1)^2 + (1)^2)| = +- ("k" + 3)/sqrt(3)`

Now, `sqrt(3) = +- 1/2 (("k" + 3)/sqrt(3))` .....(given)

⇒ 6 = `+- ("k" + 3)`

⇒ k = 3, – 9