Question 1320

Vectors II: Lines and Planes

2020 Paper 1 Question 1 Variant

Question

A plane

{\pi_1}

contains two vectors

{\begin{pmatrix} 1 \\ 0 \\ 4 \end{pmatrix}}

and

{\begin{pmatrix} 1 \\ 1 \\ 1 \end{pmatrix}.}

(i)

Find a vector normal to

{\pi_1.}

[2]

A plane

{\pi_2}

has equation

{x + 2 y - z = 0.}

(ii)

Find the acute angle between

{\pi_1}

and

{\pi_2.}

[2]