Write the value of k for which the line is perpendicular to the normal to the plane .

Equation of the line in Cartesian form is given as,

So, the direction cosines of the line are given as,

The equation of the plane is, so, we have the vector normal to the plane as,

It is required that, the line should be perpendicular to the normal to the plane , so, we should have,

(2⨯2) + (3⨯3) + (k⨯4)=0

4 + 9 + 4k=0

13 + 4k=0

4k= - 13

Hence, for the line will be perpendicular to the normal to the plane

.