Statement I : If dot product and cross product of $\vec{A} and \vec{B} are zero, it implies that one of the vector \vec{A} and \vec{B} must be a null vector.$
Statement II : Null vector is a vector with zero magnitude.

Moderate

A

If both statement I and statement II are true and statement II is the correct explanation of statement I.
B

If both statement I and statement II are true but statement II is not the correct explanation of statement I.
C

If statement I is true but statement II is false.
D

If both statement I and statement II are false.

Solution

$\vec{A} . \vec{B} = | \vec{A |} | \vec{B |} cosθ = 0$
$\vec{A} \times \vec{B} = | \vec{A |} | \vec{B |} sinθ = 0$
If $\vec{A} and \vec{B}$ are not null vectors then it follows that $sinθ and cosθ$ both should be zero simultaneously. But it cannot be possible so it is essential that one of the vector must be null vector.

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