Question

A:The sum and difference of two vectors will be equal in magnitude when two vectors are perpendicular to each other.
B:The sum and difference of two vectors will have the same direction, when the vectors have unequal magnitudes but are in the same direction.

• A. Both A and B are true
• B. A is true but B is false
• C. B is true but A false
• D. Both A and B are false

Answer 1

Answer: (B)

A is true but B is false

As we know the resultant of two vector can be written as

$V_{Resultant}=\sqrt{V_1^2+V_2^2+V_1{V}_{2}cos\theta }$

Now $\theta ={90}^0$ $cos90=0$

Hence A is correct.

The sub and difference of two vectors will not have the same direction, when the two vectors have unequal magnitudes but in the same direction. Because the resultant of of sum of two vectors will be the opposite of the resultant of subtraction of two vectors. Hence B is wrong.