Question

If \[ \frac{x+3}{a}=\frac{y-1}{b}=\frac{z}{c} \] is the common line of the two perpendicular planes \[ 2x+3y+4z+d=0 \] and \[ x+py+z+5=0, \] then \(p+d=\)

• A. \(-5\)
• B. \(1\)
• C. \(-4\)
• D. \(2\)

Hint:

If a line is common to two planes, every point on the line satisfies both plane equations. Substitute the given point first, then use the perpendicular condition \[ \boxed{\vec n_1\cdot\vec n_2=0} \] to verify the result.

Answer 1

The Correct Option is B