Question 1320

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

Question

A plane π1{\pi_1} contains two vectors (520){\begin{pmatrix} 5 \\ 2 \\ 0 \end{pmatrix}} and (525).{\begin{pmatrix} - 5 \\ - 2 \\ 5 \end{pmatrix}.}
(i)
Find a vector normal to π1.{\pi_1.}
[2]
A plane π2{\pi_2} has equation 3x+3y2z=0.{- 3 x + 3 y - 2 z = 0.}
(ii)
Find the acute angle between π1{\pi_1} and π2.{\pi_2.}
[2]

Answer