Q5. How many unit vectors are collinear with a given nonzero vector a?
Two: â, along a, and −â, opposite to it. Both have magnitude 1 and lie along lines parallel to a.
Q6. Is the zero vector a unit vector? Can two unit vectors be unequal?
No: 0 has magnitude 0, not 1. Yes: unit vectors have the same magnitude but may point in different directions, like â and −â.
Q7. In the regular hexagon ABCDEF with centre O, name four vectors that are negatives of AB.
BA, DE, CO and OF: each has the length of a side and points opposite to AB.
Q8. Two vectors are coinitial and equal. What can you say about their terminal points?
They coincide: from the same initial point, the same length in the same direction ends at the same point. So the two directed line segments are the same.
Q9. A man walks 40 km, 30° east of north, and then 40 km, 30° west of south. Draw both displacements to scale. Where does he end up?
The second arrow, started at the tip of the first, has the same length and the opposite direction, so it brings him back to O. The two displacements are negatives of each other, and together they make the zero vector.
Q10. Beyond the NCERT text (JEE): if a is collinear with b and b is collinear with c, must a be collinear with c?
Yes if b ≠ 0, since a and c are then parallel to the line of b. If b = 0, no: NCERT lets 0 have any direction, so it is collinear with every vector, and a and c can be any two vectors.