Question 1320

Vectors II: Lines and Planes
2020 Paper 1 Question 1 Variant

Question

A plane π1{\pi_1} contains two vectors (131){\begin{pmatrix} - 1 \\ - 3 \\ 1 \end{pmatrix}} and (331).{\begin{pmatrix} 3 \\ 3 \\ 1 \end{pmatrix}.}
(i)
Find a vector normal to π1.{\pi_1.}
[2]
A plane π2{\pi_2} has equation 4x+5y+3z=0.{4 x + 5 y + 3 z = 0.}
(ii)
Find the acute angle between π1{\pi_1} and π2.{\pi_2.}
[2]

Answer