i'm looking at past year papers for sections which i can't do and i dont know how to do this question. i need to know under what topic is this and if possible how to get to the answer as well so i have an example to figure out how it goes. The answer is at the bottom. Thanks.

(a) We are given a point A(1, 1, 0) and the line

l : (x − 1)/2= y =(2 − z)/3

(i) Find a vector, v, parallel to l.

(ii) Find the cartesian equation of the plane that contains A and l.

(b) Two vectors are given by a = (0, 1,−1) and b = (1,−1, 0). Determine the area of the parallelogram with edges a and b.

ANSWER:

(a)(i) v = (2, 1,−3)

(ii) A point on the line is P(1, 0, 2)

->

AP × v =

i j k

0 −1 2

2 1 −3

= i + 4j + 2k

The equation is therefore of the form

x + 4y + 2z = d

As A is in the plane, the equation is

x + 4y + 2z = 5

(b)

a × b =

i j k

0 1 −1

1 −1 0

= −i − j − k

Area = ||a × b|| =sqrt(3)