SOLUTION: Find the point P on the plane 0x+1y-3z=8 closest to the point Q(2,-3,3). P = ( , , )????? Thank you guys!

Question 62449: Find the point P on the plane 0x+1y-3z=8 closest to the point Q(2,-3,3).
P = ( , , )?????
Thank you guys!

Answer by venugopalramana(3286) (Show Source): You can put this solution on YOUR website!
Find the point P on the plane 0x+1y-3z=8 closest to the point Q(2,-3,3).
P = ( , , )?????(p,q,r) say
it on plane.hence
q-3r=8...............1
PQ is perpenicular to plane...or parallel to its normal
drs of plane = (0,1,-3)
drs of PQ = [p-2,q+3,r-3]
(p-2)/0 = (q+3)/1 = (r-3)/-3
p=2
r-3 = -3(q+3)=-3q-9
3q+r=-6..............2
3*eqn.1-en.2
-10r=30
r=-3
3q=-3
q=-1
hence p is (2,-1,-3)

Thank you guys!
RELATED QUESTIONS
Find the point on the line y=4x that is closest to the point P=(1,2). (answered by Boreal,MathLover1,ikleyn)

Hi you guys, i need help with this question for sat or sunday, thank you very much.... (answered by venugopalramana)

Find the distance from the point Q(-3,-3,-8) to the line which passes through the point... (answered by venugopalramana)

please help asap! love you guys! Find the distance from the point P=(0,0,4) to the... (answered by venugopalramana)

Find a distance from the point P(3,5) to the line x= -2 Or Find the distance from... (answered by stanbon)

Find the vector v with initial point P and terminal point Q. P(6, −1, 0), Q(0, −2,... (answered by MathLover1,math_tutor2020)

Find the point on the line -3 x + 4 y + 3 =0 which is closest to the point... (answered by Fombitz)

Find the point on the line y=2x+3 that is closest to... (answered by Alan3354)

A man is on a lake in a canoe one kilometer from the closest point P of a straight shore... (answered by ankor@dixie-net.com)