If vec{a} = a_1hat{i} + a_2hat{j} + a_3hat{k} | vedclass

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(B) Two vectors $\vec{a}$ and $\vec{b}$ are parallel if and only if there exists a non-zero scalar $k$ such that $\vec{a} = k\vec{b}$.Substituting the

Vedclass · Accepted Answer

$\frac{a_1}{b_1} = \frac{a_2}{b_2} = \frac{a_3}{b_3}$

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(B) Two vectors $\vec{a}$ and $\vec{b}$ are parallel if and only if there exists a non-zero scalar $k$ such that $\vec{a} = k\vec{b}$.Substituting the components,we have $a_1\hat{i} + a_2\hat{j} + a_3\hat{k} = k(b_1\hat{i} + b_2\hat{j} + b_3\hat{k})$.Comparing the coefficients of $\hat{i}, \hat{j},$ and $\hat{k}$,we get $a_1 = kb_1, a_2 = kb_2,$ and $a_3 = kb_3$.This implies $\frac{a_1}{b_1} = \frac{a_2}{b_2} = \frac{a_3}{b_3} = k$.Thus,the correct condition for parallel vectors is $\frac{a_1}{b_1} = \frac{a_2}{b_2} = \frac{a_3}{b_3}$.

If $\vec{a} = a_1\hat{i} + a_2\hat{j} + a_3\hat{k}$ and $\vec{b} = b_1\hat{i} + b_2\hat{j} + b_3\hat{k}$ are parallel vectors,then which of the following is true?

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