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  4. The magnitude of a vector, on the addition of two vectors 6 veci+7 vecj and 3 veci+4 vecj, is :

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Q. The magnitude of a vector, on the addition of two vectors $ 6\vec{i}+7\vec{j} $ and $ 3\vec{i}+4\vec{j}, $ is :

WBJEEWBJEE 2006

Solution:

Given, $ \vec{A}=\hat{6}+7\hat{j}+0\hat{k} $ and $ \vec{B}=3\hat{i}+4\hat{j}+0\hat{k} $ Sum of two vectors $ =\vec{A}+\vec{B} $ $ =(6\hat{i}+7\hat{j}+0\hat{k})+(3\hat{i}+4\hat{j}+0\hat{k}) $ $ =(6\,+3)\,\hat{i}+(7+4)\hat{j}+(0+0)\hat{k} $ $ =9\hat{i}+11\hat{j} $ Therefore, magnitude of the sum of twovectors $ =\sqrt{{{(9)}^{2}}+{{(11)}^{2}}} $ $ =\sqrt{81+121} $ $ =\sqrt{202} $