Question

The equation of the plane passing through

mid-point of the joining the points P(3, 4, 5) and

Q(1, 2, 3) and which is perpendicular to PQ is –

• A. 2x + 3y + 4z = – 9
• B. x + y + z = 9
• C. 2x + 3y + 4z = 9
• D. x + y + z = – 9

Answer 1

Answer: (B)

x + y + z = 9

Answer 2

P(3, 4, 5)

Q (1, 2, 3)

Mid-point of the line PQ

Ž $R\left( \frac{3 + 1}{2},\frac{4 + 2}{2},\frac{5 + 3}{2} \right)$

Ž R(2, 3, 4) = (x₁, y₁, z₁)

DR's of normal = DR's of line PQ

Ž (3 – 1), (4 – 2), (5 – 3)

Ž 2, 2, 2,

Ž 1, 1, 1

Ž a, b, c

Eq. of the plane which is passing through the point R

Ž a (x – x₁) + b(y – y₁) + c (z – z₁) = 0