Q16 of 181 Page 1251

Mark against the correct answer in each of the following:

If the plane 2x – y + z = 0 is parallel to the line then the value of a is


Given: Plane 2x – y + z = 0 is parallel to the line



To find: value of a


Formula Used: If two lines with direction ratios a1:a2:a3 and b1:b2:b3 are perpendicular, then


a1b1 + a2b2 + a3b3 = 0


Explanation:


Since the plane is parallel to the line, the normal to the plane will be perpendicular to the line.


Equation of the line can be rewritten as



Direction ratio of the normal to the plane is 2 : -1 : 1


Direction ratio of line is 1 : -2 : a


Therefore,


2 + 2 + a = 0


a = -4


Therefore, a = -4

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