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Rubentheran · Mar 21, 2011, 09:04 AM

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

jcaron2 · Mar 21, 2011, 10:14 AM

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.

Rubentheran · Mar 21, 2011, 08:26 PM

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

jcaron2 · Mar 21, 2011, 08:33 PM

Yes! Good job.