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Addition of Vectors

The figure fo...

Question

The figure formed by the four points i + j - k, 2i + 3j, 3i + 5j -2k and k - j is

A

Rectangle

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B

Trapezium

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C

Parallelogram

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D

None of these

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Solution

The correct option is D Trapezium
$\begin{matrix} A B = \to i + 2 \to j + \to k B C = \to i + 2 \to j - 2 \to k C D = - 3 \to i - 6 \to j + 3 \to k D A = \to i + 2 \to j - 2 \to k ∴ B C = D A a n d B C ∥ D A a n d A B i s n o t p a r a l l e l t o C D ∴ p o i n t m a d e a t r a p e z i u m H e n c e, o p t i o n B i s c o r r e c t a n s w e r \end{matrix}$

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Q. Find the area of the parallelogram determined by the vectors:
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[\vec{a} \vec{b} \vec{c}]

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