If P→=i^+j^ and Q→=2i^−k^ are two vectors which when added to R→ gives a unit vector along Z-axis direction. Then R→ is

P→=i^+j^;Q→=2i^−k^; given P→+Q→+R→=k^R→=k^−(P→+Q→)=k^−(3i^+j^−k^)=−3i^−j^+2k^

If P→=i^+j^ and Q→=2i^−k^ are two vectors which when added to R→ gives a unit vector along Z-axis direction. Then R→ is

P→=i^+j^;Q→=2i^−k^; given P→+Q→+R→=k^R→=k^−(P→+Q→)=k^−(3i^+j^−k^)=−3i^−j^+2k^

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If $\vec{P} = \hat{i} + \hat{j} and \vec{Q} = 2 \hat{i} - \hat{k}$ are two vectors which when added to $\vec{R}$ gives a unit vector along Z-axis direction. Then $\vec{R}$ is

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$3 \hat{i} + \hat{j} - 2 \hat{k}$

$- 3 \hat{i} - \hat{j} + 2 \hat{k}$

$- \hat{k}$

$\hat{k}$

answer is A.

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Detailed Solution

$\vec{P} = \hat{i} + \hat{j}; \vec{Q} = 2 \hat{i} - \hat{k}; given \vec{P} + \vec{Q} + \vec{R} = \hat{k}$

$\vec{R} = \hat{k} - (\vec{P} + \vec{Q}) = \hat{k} - (3 \hat{i} + \hat{j} - \hat{k}) = - 3 \hat{i} - \hat{j} + 2 \hat{k}$

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If P→=i^+j^ and Q→=2i^−k^ are two vectors which when added to R→ gives a unit vector along Z-axis direction. Then R→ is

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If $\vec{P} = \hat{i} + \hat{j} and \vec{Q} = 2 \hat{i} - \hat{k}$ are two vectors which when added to $\vec{R}$ gives a unit vector along Z-axis direction. Then $\vec{R}$ is