NIMCET 2011 — Mathematics PYQ

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Question

NIMCET 2011 — Mathematics PYQ

NIMCET | Mathematics | 2011

$ABCD$ is a parallelogram with $\vec{AC}$ and $\vec{BD}$ as diagonals. Then, $\vec{AC} - \vec{BD}$ is equal to:

Choose the correct answer:

Explanation

1. Represent Diagonal $\vec{AC}$ :

In $\Delta ABC$ , by the triangle law of vector addition:

\vec{AC} = \vec{AB} + \vec{BC}

2. Represent Diagonal $\vec{BD}$ :

In $\Delta ABD$ , by the triangle law of vector addition:

\vec{AD} + \vec{DB} = \vec{AB} \implies \vec{DB} = \vec{AB} - \vec{AD}

However, it is easier to look at $\Delta BCD$ or $\Delta ABD$ to find $\vec{BD}$ :

\vec{BD} = \vec{AD} - \vec{AB}

Since in a parallelogram $ABCD$ , the opposite side $\vec{AD} = \vec{BC}$ :

\vec{BD} = \vec{BC} - \vec{AB}

3. Calculate the difference $\vec{AC} - \vec{BD}$ :

Substitute the expressions from Step 1 and Step 2:

\vec{AC} - \vec{BD} = (\vec{AB} + \vec{BC}) - (\vec{BC} - \vec{AB})

4. Simplify the expression:

\vec{AC} - \vec{BD} = \vec{AB} + \vec{BC} - \vec{BC} + \vec{AB}

\vec{AC} - \vec{BD} = \vec{AB} + \vec{AB}

\vec{AC} - \vec{BD} = 2\vec{AB}

Conclusion:

The expression simplifies to $2\vec{AB}$ .

The correct option is (c).

Choose the correct answer:

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