Question

The plane p has equation 3x+2y+4z=13. A second plane q is perpendicular to p and has equation ax+y+z=4 where a is constant.

Find the value of a

The line with equation r=j-k+t(i+2j+2k) meets the plane p at the point A and the plane Q at the point B. Find the length of AB

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Thanks in advance :)

Answer 1

Alright, since the planes are perpendicular the dot product of the directional vectors of the planes must be 0. So let A=<3,2,4> be the directional vector of the first plane, and let B=<a,1,1>. Then,

\[A \cdot B=0 \] and solve for a.

I hope that helps, let me know if you need help for the second part after this.