darsh Plane PI has eqn 5x+4y-2z=14. Plane P is perpendicular to PI and has eqn ax+3y+z=16. Find the value of a.? sponsored 3 months ago 2

## Answers

If the planes are perpendicular, so are their normal vectors. The dot product of the normal vectors must equal zero.

<5, 4, -2> · <a, 3, 1> = 0

5a + (4)(3) + (-2)(1) = 0

a = -2

The dot product <5,4,-2> . <a,3,1> must be 0 so 5a+12-2=0 so a=-2