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Comparing Vectors

If the vector...

Question

If the vectors $^i -^j,^j +^k$ and $^a$ form a triangle, then $^a$ may be

A

-^i -^k

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B

^i - 2^j -^k

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C

2^i +^j +^k

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D

^i +^k

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Solution

The correct option is A $-^i -^k$
$\to A B =^i -^j$ $, \to C B =^j -^k$ $, \to C A =^a$
$\to A B$ $+ \to B C$ $+ \to C A$ $= \to b$ $- \to a$ $+ \to c$ $- \to b$ $+ \to a$ $- \to c = 0$
$⟹^i -^j +^j +^k +^a = 0 ⟹^a = -^i -^k$

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