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Q.

Assertion : Magnitude of the resultant of two vectors may be less than the magnitude of either vector.
Reason : The resultant of two vectors is obtained by means of law of parallelogram of vectors.

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a

If both assertion and reason are true but reason is not the correct explanation of assertion.

b

If assertion is true but reason is false.

c

If both assertion and reason are false.

d

If both assertion and reason are true and reason is the correct explanation of assertion.

answer is B.

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Detailed Solution

If $\vec{a}$ and $\vec{b}$ are inclined at an angle greater than $90 °$ , their resultant has magnitude,

$R = \sqrt{a^{2} + b^{2} + 2 a b \cos θ}$

which is less than both $a$ and $b$ , when they are nearly equal.

Resultant of two vectors are obtained by law of parallelogram of vectors.

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Assertion : Magnitude of the resultant of two vectors may be less than the magnitude of either vector. Reason : The resultant of two vectors is obtained by means of law of parallelogram of vectors.