Given two vectors A and B where A=-5i+3j-k and B=8i-3j+4k.
Find

1)(A-2b).3k
2)the direction of cosines of A
3)vector projection of A on B
4)the equation of plane perpendicular to B

I know how to do everything from 1 to 3 except for 4.Can someone teach me only number 4.Thanks.Pleassss

The equation of a plane can be written as

A(x- x_0)+ B(y-y_0)+ C(z-z_0)= 0,

where A\vec{i}+ B\vec{j}+ C\vec{k} is a vector perpendicular to the plane and (x_0, y_0, z_0) is a point on the plane.

In this case, you're not told that the plane has to contain any particular point, so you can just choose (x_0, y_0, z_0)=(0,0,0). That makes the equation pretty simple.

So which want is the answer sir for my question.Is it 8x-3y+4z =0 ? Is this correct ?

Yes! Good job.