JEE PHYSICS MCQ: MOTION IN PLANE

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Analyzing +4 | -1

Consider the following statements about three vectors

\overrightarrow{{a}}, \overrightarrow{{b}}

and

\overrightarrow{{c}}

that have non-zero magnitudes. It follows

\overrightarrow{{b}}=\overrightarrow{{c}}

(i) if

\overrightarrow{\mathrm{a}} \cdot \overrightarrow{\mathrm{b}}=\overrightarrow{\mathrm{a}} \cdot \overrightarrow{\mathrm{c}}

(ii) if

\vec{a} \times \vec{b}=\vec{a} \times \vec{c} \quad \vec{b}

must be perpendicular to

\overrightarrow{\mathrm{c}}

View answer and explanation

Correct option: C

(i) only

Option B is correct because neither statement (i) nor (ii) necessarily implies that

\overrightarrow{{b}}=\overrightarrow{{c}}

when dealing with dot and cross products of vectors.

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