Question

Find the line through

(9, 1, −6)
that intersects and is perpendicular to the line
x = −1 + t, y = −3 + t, z = −1 + t.

Answer 1

Find the line through =(2,4,7) that intersects and is perpendicular to the line : =−1+,=−2+3,=4

I set up a system of equations and obtained :

−1+=0+2−2+3=0+44=0+7

Solving for each and putting them I obtain the vector 1=<−3,3−6,−3> I then set the direction vector as 2=<1,3,4>

Since 1⋅2=0 means they are orthogonal I obtain :

<−3,3−6,−3>⋅<1,3,4>=0

Multiplying out and solving for t I get =10/21

Explanation: