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5

Answer the following as true or false:

i. and are collinear.

ii. Two collinear vectors are always equal in magnitude.

iii. Zero vector is unique.

iv. Two vectors having same magnitude are collinear.

v. Two collinear vectors having the same magnitude are equal.

1

Find the position vector of a point R which divides the line joining the two points P and Q with position vectors and respectively in the ratio 1 : 2 internally and externally.

1

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

4

A vector is inclined at equal acute angles to x – axis, y – axis, and z - axis. If units, find

4

Write in the simplified form.

27

If and find