Write down the magnitude of each of the following vectors:

Find a unit vector in the direction of the vector:

A.

B.

C.

D.

If then find the value of λ so that may be a unit vector.

If and then find the unit vector in the direction of

If and then find a unit vector in the direction of

If and then find a unit vector parallel to

Find a vector of magnitude 9 units in the direction of the vector

Find a vector of magnitude 8 units in the direction of the vector

Find a vector of magnitude 21 units in the direction of the vector

If and find

If A(-2, 1, 2) and B(2, -1, 6) are two given points, find a unit vector in the direction of

Find the direction ratios and direction cosines of the vector

Find the direction ratios and the direction cosines of the vector joining the points A(2, 1, -2) and B(3, 5, -4).

Show that the points A, B and C having position vectors and respectively, are collinear.

The position vectors of the points A, B and C are and respectively. Show that the points A, B and C are collinear.

If the position vectors of the vertices A, B and C of a ∆ABC be and respectively, prove that ∆ABC is equilateral.

Show that the points A, B and C having position vectors and respectively, form the vertices of a right-angled triangle.

Using vector method, show that the points A(1, -1, 0), B(4, -3, 1) and C(2, -4, 5) are the vertices of a right-angled triangle.

Find the position vector of the point which divides the join of the points and (i) internally and (ii) externally in the ratio 2 : 3.

The position vectors of two points A and B are and respectively. Find the position vector of a point C which divides AB externally in the ratio 1 : 2. Also, show that A is the mid-point of the line segment CB.

Find the position vector of a point R which divides the line joining A(-2, 1, 3) and B(3, 5, -2) in the ratio 2 : 1 (i) internally (ii) externally.

Find the position vector of the mid-point of the vector joining the points and

If and A(1, 2, -1) is the given point, find the coordinates of B.

Write a unit vector in the direction of where P and Q are the points (1, 3, 0) and (4, 5, 6) respectively.