Question 1320

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

Question

A plane π1{\pi_1} contains two vectors (101){\begin{pmatrix} 1 \\ 0 \\ - 1 \end{pmatrix}} and (354).{\begin{pmatrix} 3 \\ 5 \\ - 4 \end{pmatrix}.}
(i)
Find a vector normal to π1.{\pi_1.}
[2]
A plane π2{\pi_2} has equation xy+2z=0.{- x - y + 2 z = 0.}
(ii)
Find the acute angle between π1{\pi_1} and π2.{\pi_2.}
[2]

Answer