Find the magnitude and direction of the vector $\vec{A} = \hat{i} + \hat{j}$.
- AMagnitude = $\sqrt{2}$,Direction = $45^{\circ}$ with $x$-axis
- BMagnitude = $2$,Direction = $30^{\circ}$ with $x$-axis
- CMagnitude = $\sqrt{2}$,Direction = $90^{\circ}$ with $x$-axis
- DMagnitude = $1$,Direction = $45^{\circ}$ with $x$-axis
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$ABCDEF$ is a regular hexagon and forces represented in magnitude and direction by $\overrightarrow{AB}, \overrightarrow{AC}, \overrightarrow{AD}, \overrightarrow{AE}$ and $\overrightarrow{AF}$ act at point $A$. Their resultant is:
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View SolutionFor the components of a vector $\vec{A} = (3 \hat{i} + 4 \hat{j} - 5 \hat{k})$,match the following columns.
Column $I$ Column $II$ $(A)$ Component along $x$-axis $(p)$ $5 \text{ unit}$ $(B)$ Component along vector $(2 \hat{i} + \hat{j} + 2 \hat{k})$ $(q)$ $4 \text{ unit}$ $(C)$ Component along $(6 \hat{i} + 8 \hat{j} - 10 \hat{k})$ $(r)$ $0$ $(D)$ Component along $(-3 \hat{i} - 4 \hat{j} + 5 \hat{k})$ $(s)$ None
| Column $I$ | Column $II$ |
|---|---|
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| $(B)$ Component along vector $(2 \hat{i} + \hat{j} + 2 \hat{k})$ | $(q)$ $4 \text{ unit}$ |
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| $(D)$ Component along $(-3 \hat{i} - 4 \hat{j} + 5 \hat{k})$ | $(s)$ None |
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View SolutionWhich of the following quantity/quantities are dependent on the choice of orientation of the co-ordinate axes?
$(a)$ $\vec{a}+\vec{b}$
$(b)$ $3a_x+2b_y$
$(c)$ $(\vec{a}+\vec{b}-\vec{c})$
$(a)$ $\vec{a}+\vec{b}$
$(b)$ $3a_x+2b_y$
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