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Multiplication with Vectors

Find A×B, if ...

Question

Find $\to A \times \to B$ , if $\to A = 2^i -^j + 3^k$ and $\to B = - 2^i + 3^j + 4^k$

A

- 13^i - 14^j - 4^k

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B

5^i + 14^j + 4^k

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C

5^i - 14^j + 4^k

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D

- 13^i - 14^j + 4^k

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Solution

The correct option is D $- 13^i - 14^j + 4^k$
We have
$\to A = 2^i -^j + 3^k$ and $\to B = - 2^i + 3^j + 4^k$
So,
$\to A \times \to B = (- 4 - 9)^i - (8 - (- 6))^j + (6 - 2)^k$
$= - 13^i - 14^j + 4^k$

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\to a = 2^i + 3^j - 4^k, \to b =^i +^j +^k

\to c = 4^i + 2^j + 3^k,

∣ ∣ ∣ \to a \times (\to b \times \to c) ∣ ∣ ∣ =

\to A \times \to B

\to A = 2^i -^j + 3^k

\to B = - 2^i + 3^j + 4^k

\to a = 2^i + 3^j - 4^k

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

\to c = 4^j + 3^k

| (¯ ¯ ¯ a \times ¯ ¯ b) \times ¯ ¯ c |

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If $\to a$ and $\to b$ are vectors such that $| \to a + \to b | = \sqrt{29}$ and $\to a \times (2^i + 3^j + 4^k) = (2^i + 3^j + 4^k) \times \to b,$ then a possible value of $(\to a + \to b) . (- 7^i + 2^j + 3^k)$ is

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