Question

If A and B are foot of perpendicular drawn from point Q(a, b, c) to the planes yz and zx, then equation of plane through the points A, B and O is ______.

Options

• `x/a + y/b - z/c` = 0

• `x/a - y/b + z/c` = 0

• `x/a - y/b - z/c` = 0

• `x/a + y/b + z/c` = 0

Answer 1

If A and B are foot of perpendicular drawn from point Q(a, b, c) to the planes yz and zx, then equation of plane through the points A, B and O is `underlinebb(x/a + y/b - z/c = 0)`.

Explanation:

It is given that, the foot of perpendicular from point Q(a, b, c) to the yz plane is A(0, b, c) and the foot of perpendicular from point Q to the zx plane is B(a, 0, c).

Let the equation of plane passing through the point (0, 0, 0) be Ax + By + Cz = 0 ......(i)

As it is passing through the point A(0, b, c) and B(a, 0, c).

So, 0 + Bb + Cc = 0 and Aa + 0 + Cc = 0

`\implies` Cc = Bb and Cc = –Aa

Therefore, – Aa = – Bb = Cc = k

`\implies`  A = `-k/a`, B = `-k/b` and C = `k/c`

`-k/ax - k/by + k/cz` = 0  ...[From equation (i)]

`\implies - x/a - y/b + z/c` = 0 or `x/a + y/b - z/c` = 0