Vector A→ and −A→ have

Vector A→ and −A→ have equal magnitude but opposite direction A, C, D are not correct Ex: A→=2i^+2j^+2k^ in this vectori^,j^,k^ are unit vectors along+ ve x, y, z axis−A→=−2i^−2j^−2k^ . Hence −i^,−j^,−k^ are unit vectors along – ve x, y, z axis. So A→ and −A→ are equal in magnitude and its direction is opposite.

Vector A→ and −A→ have

Vector A→ and −A→ have equal magnitude but opposite direction A, C, D are not correct Ex: A→=2i^+2j^+2k^ in this vectori^,j^,k^ are unit vectors along+ ve x, y, z axis−A→=−2i^−2j^−2k^ . Hence −i^,−j^,−k^ are unit vectors along – ve x, y, z axis. So A→ and −A→ are equal in magnitude and its direction is opposite.

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Vector $\vec{A} and - \vec{A}$ have

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equal magnitude and same direction

equal magnitude but opposite direction

unequal magnitude but same direction

both direction and magnitude are not same

answer is B.

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Detailed Solution

Vector

\vec{A} and - \vec{A}

have equal magnitude but opposite direction A, C, D are not correct

Ex: $\vec{A} = 2 \hat{i} + 2 \hat{j} + 2 \hat{k}$ in this vector $\hat{i}, \hat{j}, \hat{k}$ are unit vectors along+ ve x, y, z axis $- \vec{A} = - 2 \hat{i} - 2 \hat{j} - 2 \hat{k}$ . Hence $- \hat{i}, - \hat{j}, - \hat{k}$ are unit vectors along – ve x, y, z axis. So $\vec{A} and - \vec{A}$ are equal in magnitude and its direction is opposite.