Q. 6

Mark against the correct answer in each of the following:

If the line is parallel to the plane 2x – 3y + kz = 0, then the value of k is

A.

B.

C.

D.

Answer :

Given:


1. Equation of line is


2. Equation of plane is 2x – 3y + kz = 0


Formula Used: If two direction ratios are perpendicular, then


a �1a2 + b1b2 + c1c2 = 0


Explanation:


Direction ratios of given line is (3, 4, 5)


Direction ratios of given plane is (2, -3, k)


Since the given line is parallel to the plane, the normal to the plane is perpendicular to the line.


So direction ratio of line is perpendicular to direction ratios of plane.


3× 2 + 4× -3+ 5× k = 0


6 – 12 + 5k = 0



Therefore,

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