Question 1320

Vectors II: Lines and Planes

2020 Paper 1 Question 1 Variant

Question

A plane

{\pi_1}

contains two vectors

{\begin{pmatrix} - 1 \\ - 1 \\ 2 \end{pmatrix}}

and

{\begin{pmatrix} - 3 \\ 3 \\ - 4 \end{pmatrix}.}

(i)

Find a vector normal to

{\pi_1.}

[2]

A plane

{\pi_2}

has equation

{5 x + 4 y + z = 0.}

(ii)

Find the acute angle between

{\pi_1}

and

{\pi_2.}

[2]