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)