Statement I : If $\vec{i} and \hat{j}$ are unit vectors along x-axis and y-axis respectively, the magnitude of vector $\hat{i} + \hat{j}$ will be $\sqrt{2}$ .
Statement II : Unit vector are used to indicate a direction only.

Moderate

A

If both statement I and statement II are true and statement II is the correct explanation of statement I.
B

If both statement I and statement II are true but statement II is not the correct explanation of statement I.
C

If statement I is true but statement II is false.
D

If both statement I and statement II are false.

Solution

Since $\hat{i} and \hat{j}$ are unit vectors, their magnitude are $| \hat{i} | = 1 and | \hat{j} | = 1 .$ Magnitude of resultant vector is equal to $\sqrt{| i |^{2} + | j |^{2}} = \sqrt{{(1)}^{2} + {(1)}^{2}} = \sqrt{2}$

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