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Question: Let \(\vec { A } = 2 \hat { i } + \hat { j } , B = 3 \hat { j } - \hat { k }\) and \(\vec { C } =...

Let A⃗=2i^+j^,B=3j^−k^\vec { A } = 2 \hat { i } + \hat { j } , B = 3 \hat { j } - \hat { k } and C⃗=6i^−2k^\vec { C } = 6 \hat { i } - 2 \hat { k } value of A⃗−2B⃗+3C⃗\vec { A } - 2 \vec { B } + 3 \vec { C } would be

A

20i^+5j^+4k^20 \hat { i } + 5 \hat { j } + 4 \hat { k }

B

20i^−5j^−4k^20 \hat { i } - 5 \hat { j } - 4 \hat { k }

C

4i^+5j^+20k^4 \hat { i } + 5 \hat { j } + 20 \hat { k }

D

5i^+4j^+10k^5 \hat { i } + 4 \hat { j } + 10 \hat { k }

Answer

20i^−5j^−4k^20 \hat { i } - 5 \hat { j } - 4 \hat { k }

Explanation

Solution

A⃗−2B⃗+3C⃗=(2i^+j^)−2(3j^−k^)+3(6i^−2k^)\vec { A } - 2 \vec { B } + 3 \vec { C } = ( 2 \hat { i } + \hat { j } ) - 2 ( 3 \hat { j } - \hat { k } ) + 3 ( 6 \hat { i } - 2 \hat { k } )

=2i^+j^−6j^+2k^+18i^−6k^= 2 \hat { i } + \hat { j } - 6 \hat { j } + 2 \hat { k } + 18 \hat { i } - 6 \hat { k }

=20i^−5j^−4k^20 \hat { i } - 5 \hat { j } - 4 \hat { k }