Question

If $ \overrightarrow{A}=4\hat{i}+8\hat{j}-\hat{k},\overrightarrow{B}=3\hat{i}+2\hat{j}-\hat{k} $ and $ \overrightarrow{C}=5\hat{i}+4\hat{j}+\hat{k}, $ then $ \overrightarrow{A}.(\overrightarrow{B}.\overrightarrow{C}) $ is equal to

• A. $ 88\hat{i}+176\hat{j}-22\hat{k} $
• B. $ 22\hat{i}+44\hat{j}-11\hat{k} $
• C. $ \hat{i}+4\hat{j}-\hat{k} $
• D. None of these

Answer 1

Answer: (A)

Given, $ \overrightarrow{A}=4\hat{i}+8\hat{j}-\hat{k}, $
$ \overrightarrow{B}=3\hat{i}+2\hat{j}-\hat{k} $ and $ \overrightarrow{C}=5\hat{i}+4\hat{j}+\hat{k} $
Now, $ \overrightarrow{B}.\overrightarrow{C}=(3\hat{i}+2\hat{j}-\hat{k}).(5\hat{i}+4\hat{j}+\hat{k}) $
$ =15+8-1 $ $ =22 $
$ \therefore $ $ \overrightarrow{A}.(\overrightarrow{B}.\overrightarrow{C})=(4\hat{i}+8\hat{j}-\hat{k}).22 $
$ =88\hat{i}+176\hat{j}-22\hat{k} $