If $straight a with rightwards arrow on top comma space straight b with rightwards arrow on top comma space straight c with rightwards arrow on top space and space straight d with rightwards arrow on top$ are distinct non-zero vectors represented by directed lines from the origin to the points A, B, C and D respectively and if $straight b with rightwards arrow on top minus straight a with rightwards arrow on top space equals space straight c with rightwards arrow on top space minus space straight d with rightwards arrow on top$ , then prove that ABCD is a parallelogram.

Solution

Here $straight a with rightwards arrow on top comma space straight b with rightwards arrow on top comma space straight c with rightwards arrow on top comma space straight d with rightwards arrow on top$ are the position vectors of A, B, C, D respectively with reference to O as origin
Now, $straight b with rightwards arrow on top minus straight a with rightwards arrow on top space equals space straight c with rightwards arrow on top minus straight d with rightwards arrow on top$
$rightwards double arrow space space space space space space OB with rightwards arrow on top space minus space OA with rightwards arrow on top space equals space OC with rightwards arrow on top space minus space OD with rightwards arrow on top rightwards double arrow space space space space space space space space space space space AB with rightwards arrow on top space equals space DC with rightwards arrow on top therefore space space space space space space AB space equals space DC space and space AB vertical line vertical line DC therefore space space space space space ABCD space is space straight a space parallelogram.$

Some More Questions From Vector Algebra Chapter

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Vector Algebra

Some More Questions From Vector Algebra Chapter

Classify the following measures as scalars and vectors.
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Vector Algebra

If are distinct non-zero vectors represented by directed lines from the origin to the points A, B, C and D respectively and if , then prove that ABCD is a parallelogram.

Some More Questions From Vector Algebra Chapter

Classify the following measures as scalars and vectors.20 m/s2

Classify the following measures as scalars and vectors.time period

Classify the following measures as scalars and vectors.distance

Classify the following measures as scalars and vectors.force

Classify the following measures as scalars and vectors.velocity

Classify the following measures as scalars and vectors.work done

Mock Test Series

NCERT Sample Papers

Entrance Exams Preparation

Classify the following measures as scalars and vectors.
20 m/s²

Classify the following measures as scalars and vectors.
time period

Classify the following measures as scalars and vectors.
distance

Classify the following measures as scalars and vectors.
force

Classify the following measures as scalars and vectors.
velocity

Classify the following measures as scalars and vectors.
work done