In the following questions, do not evaluate surds (e. g. ? 2). leave them in your answer in that form (e. g. ? ? = 1 ± ? 2).
1. (a) write down the vector equation of the line passing through the points a and b with
? ?
position vectors = + + 2? ? and = ? + 3? ? respectively. find the
cartesian equation of the line.
(b) find the vector and cartesian equations of the line passing through the point a = (3,1,2) which is parallel to the vector (-1,2,-3).
2. find the scalar product of each pair of vectors, and hence determine the angle between them:
?
(a) = + and ? ? = +
?
(b) = + and ? ? = ?
3. (a) points a=(4,1,2), b=(3,-2,1) and c=(0,1,-1) form a triangle abc. find the interior angle b
the triangle using the scalar product and an appropriate selection of the vectors
and
(b) use the vector product to find the area of the triangle.
4. (a) find the vector product of = + and ? ? = ? . comment on your answer.
)find a =+? ? and? ? =? ? .