Two vectors vec{A} and vec{B} are parallel to | vedclass

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Question

(A) Two vectors $\vec{A}$ and $\vec{B}$ are parallel if their components are proportional,meaning $\frac{A_x}{B_x} = \frac{A_y}{B_y} = \frac{A_z}{B_z}

Vedclass · Accepted Answer

$\vec{A} = 3\hat{i} + 6\hat{j} + 9\hat{k}$,$\vec{B} = \hat{i} + 2\hat{j} + 3\hat{k}$

Vedclass · Answer

(A) Two vectors $\vec{A}$ and $\vec{B}$ are parallel if their components are proportional,meaning $\frac{A_x}{B_x} = \frac{A_y}{B_y} = \frac{A_z}{B_z} = k$.For option $A$: $\frac{3}{1} = 3$,$\frac{6}{2} = 3$,$\frac{9}{3} = 3$. Since all ratios are equal to $3$,$\vec{A} = 3\vec{B}$,so they are parallel.For option $B$: $\frac{3}{1} = 3$,$\frac{-6}{2} = -3$. Ratios are not equal.For option $C$: $\frac{2}{1} = 2$,$\frac{6}{2} = 3$. Ratios are not equal.For option $D$: $\frac{2}{1} = 2$,$\frac{3}{-2} = -1.5$. Ratios are not equal.Thus,the correct option is $A$.

Column $I$	Column $II$
$(A)$ $\theta=60^{\circ}$	$(p)$ $n=\sqrt{3}$
$(B)$ $\theta=90^{\circ}$	$(q)$ $n=1$
$(C)$ $\theta=120^{\circ}$	$(r)$ $n=\sqrt{2}$
$(D)$ $\theta=180^{\circ}$	$(s)$ $n=2$

Two vectors $\vec{A}$ and $\vec{B}$ are parallel to each other if one is a scalar multiple of the other,i.e.,$\vec{A} = k\vec{B}$. Which of the following pairs of vectors are parallel?

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