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Multiplication with Vectors

If a = î + ĵ ...

Question

If $\to a =^i +^j +^k$ , and $\to b =^j -^k$ then area vector of plane formed by $\to a$ and $\to b$ is

A

^i -^j -^k

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B

^j -^k

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C

- 2^i +^j +^k

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D

2^i

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Solution

The correct option is C $- 2^i +^j +^k$
Area vector can be calculated by using the cross product of two vectors.
$(\to a \times \to b) = (^i +^j +^k) \times (^j -^k)$
$\to a \times \to b = - 2^i +^j +^k$

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Similar questions

\to a =^i +^j +^k

\to b =^j -^k

then area vector of plane formed by

\to a

\to b

\to a

is a non-zero vector, then the value of

^i \times (\to a \times^i) +^j \times (\to a \times^j) +^k \times (\to a \times^k)

\to a =^i +^j +^k

\to b =^j -^k

, find a vector

\to c

\to a \times \to c = \to b

\to a . \to c = 3

.

Q. A unit vector perpendicular to the plane containing the vector

^i + 2^j +^k

- 2^i +^j + 3^k

Q. The vectors perpendicular to

^i -^j -^k

in the plane of

^i -^j -^k

-^i +^j +^k

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