Solution1:. Given. vectors. and. the. points. (a). (i):

Solution1: Given vectors and the points
(a)
(i):
(ii):
(iii): Distance from A to B is
(iv): Since, so unit vector in the direction of is
(v) : Suppose that the point on negative y axis is which is same distance from
origin as A. This implies that
Hence, point on negative y axis is
(vi):
(vii): Given this implies that
The distance between vectors and is
And the distance between vectors and is
Hence, vector point in a direction closer to .
(viii): The vector in the direction of positive y axis is . So the angle between
vector and is
Simplify further we get
(ix): Given and . So the angle between and is

Simplify further
(b):
(i):
(ii): Given that . Suppose that
….. (1)
Where vector x is perpendicular to vector d and y is parallel to vector b. This implies that
and where m is any scalar
Now,
Implies that
…. (2)
And
Substitute the values of x and y in equation (1) we get
Compare both sides we get,
This implies that
Substitute the value of v and w in equation (2) we get
So,
Hence,