If A-2-3-k- and B-3-2-4k- then find the value of A-B- A-B-

The correct option is B 20î+10ĵ+10k̂ . A⃗ +B⃗ =[2î +3ĵ +k̂ ]+[3î +2ĵ +4̂k̂ ]=5î +5ĵ +5k̂ A⃗ B⃗ =[2î +3ĵ +k̂ ] [3î +2ĵ +4̂k̂ ]= î +ĵ 3k̂ [ ...

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Byju's Answer

Standard XII

Mathematics

Addition of Vectors

If A⃗=2î+3ĵ...

Question

If $\to A = 2^i + 3^j +^k$ and $\to B = 3^i + 2^j + 4^k$ , then find the value of $(\to A + \to B) \times (\to A - \to B)$ .

- 30^i + 10^j + 10^k

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- 20^i + 10^j + 10^k

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- 20^i + 40^j + 10^k

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- 20^i + 10^j + 60^k

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Solution

The correct option is B $- 20^i + 10^j + 10^k$ .
$\to A + \to B = [2^i + 3^j +^k] + [3^i + 2^j +^4 k] = 5^i + 5^j + 5^k$

$\to A - \to B = [2^i + 3^j +^k] - [3^i + 2^j +^4 k] = -^i +^j - 3^k$

$[\to A - \to B] \times [\to A - \to B] = \begin{matrix} ^i & ^j & ^k 5 & 5 & 5 - 1 & 1 & - 3 \end{matrix} = - 20^i + 10^j + 10^k$

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If →A=2^i+3^j+^k and →B=3^i+2^j+4^k, then find the value of (→A+→B)×(→A−→B).

The correct option is B −20^i+10^j+10^k.→A+→B=[2^i+3^j+^k]+[3^i+2^j+^4k]=5^i+5^j+5^k→A−→B=[2^i+3^j+^k]−[3^i+2^j+^4k]=−^i+^j−3^k[→A−→B]×[→A−→B]=^i^j^k555−11−3=−20^i+10^j+10^k

If $\to A = 2^i + 3^j +^k$ and $\to B = 3^i + 2^j + 4^k$ , then find the value of $(\to A + \to B) \times (\to A - \to B)$ .