Solveeit Logo
Login

Question

Question: \(\overset{\rightarrow}{A} = 2\widehat{i} + \widehat{j},B = 3\widehat{j} - \widehat{k}\) and\(\overs...

A→=2i^+j^,B=3j^−k^\overset{\rightarrow}{A} = 2\widehat{i} + \widehat{j},B = 3\widehat{j} - \widehat{k} andC→=6i^−2k^\overset{\rightarrow}{C} = 6\widehat{i} - 2\widehat{k}.

Value of A→−2B→+3C→\overset{\rightarrow}{A} - 2\overset{\rightarrow}{B} + 3\overset{\rightarrow}{C} would be

A

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

B

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

C

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

D

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

Answer

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

Explanation

Solution

A→−2B→+3C→=(2i^+j^)−2(3j^−k^)+3(6i^−2k^)\overset{\rightarrow}{A} - 2\overset{\rightarrow}{B} + 3\overset{\rightarrow}{C} = (2\widehat{i} + \widehat{j}) - 2(3\widehat{j} - \widehat{k}) + 3(6\widehat{i} - 2\widehat{k})

=2i^+j^−6j^+2k^+18i^−6k^= 2\widehat{i} + \widehat{j} - 6\widehat{j} + 2\widehat{k} + 18\widehat{i} - 6\widehat{k}=20i^−5j^−4k^20\widehat{i} - 5\widehat{j} - 4\widehat{k}