Question

The value of m for which straight line 3x-2y+z+3=0=4x-3y+4z+1 is parallel to the plane 2x-y+mz-2=0

Answer 1

Step-by-step explanation:

Direction ratios of normals to planes are (3,−2,1) and (4,−3,4) respectively.

So direction ratio of the required line is the cross product of these normals

i.e.

∣

∣

∣

∣

∣

∣

∣

∣

i

3

4

j

−2

−3

k

1

4

∣

∣

∣

∣

∣

∣

∣

∣

On expanding the determinant we get;

−5i−8j−k

Therefore, direction ratio of line is (5,8,1)

Now line is parallel to 2x−y+mz−2=0, So dot product of direction ratio of line and normal to plane must be 0

∴10−8+m=0

⇒m=−2