Statement I : If $\vec{A} . \vec{B} = \vec{B} . \vec{C}, then \vec{A} may not always be equal to \vec{C}$
Statement II : The dot product of two vectors involves cosine of the angle between the two vectors.

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

$\vec{A} . \vec{B} = \vec{B} . \vec{C} \Rightarrow {ABcosθ}_{1} = BC {cosθ}_{2}$
$∴ A = C, only when θ_{1} = θ_{2}$
So when angle between $\vec{A} and \vec{B} is equal to angle between \vec{B} and \vec{C} only when \vec{A} equal to \vec{C} .$

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