The vectors 3i + j - 5k and ai + bj - 15k are | vedclass

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(D) Two vectors $\vec{u} = a_1 i + b_1 j + c_1 k$ and $\vec{v} = a_2 i + b_2 j + c_2 k$ are collinear if their components are proportional,i.e.,$\frac

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$a = 9, b = 3$

Vedclass · Answer

(D) Two vectors $\vec{u} = a_1 i + b_1 j + c_1 k$ and $\vec{v} = a_2 i + b_2 j + c_2 k$ are collinear if their components are proportional,i.e.,$\frac{a_1}{a_2} = \frac{b_1}{b_2} = \frac{c_1}{c_2}$.Given vectors are $3i + j - 5k$ and $ai + bj - 15k$.Comparing the components,we have $\frac{3}{a} = \frac{1}{b} = \frac{-5}{-15}$.Simplifying the ratio,$\frac{-5}{-15} = \frac{1}{3}$.Therefore,$\frac{3}{a} = \frac{1}{3} \Rightarrow a = 9$.And $\frac{1}{b} = \frac{1}{3} \Rightarrow b = 3$.Thus,the correct values are $a = 9$ and $b = 3$.

The vectors $3i + j - 5k$ and $ai + bj - 15k$ are collinear if $....$

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