could you pls help me on these?

find the distance of:

(a) point P(1,3,1) to the surface of 3x+7y-5z=0

(b) point P(7,6,3) to the straight line of r=6j+k-t(i-j-k)

(c) L1:r=5k+t(3j+k) to L2:r=i+j-3k+t(i+3j+k)

thanks! =)

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- Jan 17th 2010, 01:29 AMailing418vectors distance
could you pls help me on these?

find the distance of:

(a) point P(1,3,1) to the surface of 3x+7y-5z=0

(b) point P(7,6,3) to the straight line of r=6j+k-t(i-j-k)

(c) L1:r=5k+t(3j+k) to L2:r=i+j-3k+t(i+3j+k)

thanks! =) - Jan 17th 2010, 06:42 AMearboth
to a)

The equation 3x + 7y - 5z = 0 describes a plane with it's normal vector . Transform the equation such that the normal vector is an unit vector. Plug in the coordinates of the staionary vector of P. The result is the distance of P from the plane:

to b)

Determine the equation of a plane which contains P and which is perpendicular to the line. Calculate the coordinates of the point of intersection between the line and the plane. Calculate the distance between these two points.

point of intersection

to c)

Determine the equation of a plane which contains line L1 and is parallel to line L2. Then take any point of L2 and calculate it's distance to the plane as you've done in a).

with