Question:
If
\[
\vec{a}=(p,-2,5)
\]
and
\[
\vec{b}=(1,q,-3)
\]
are collinear vectors then
If
\[
\vec{a}=(p,-2,5)
\]
and
\[
\vec{b}=(1,q,-3)
\]
are collinear vectors then
Show Hint
Two vectors are collinear if the ratios of their corresponding components are equal.
\[
\frac{a_1}{b_1}
=
\frac{a_2}{b_2}
=
\frac{a_3}{b_3}
\]
Updated On: Jun 25, 2026
- \(p=\dfrac{5}{3},\ q=\dfrac{6}{5}\)
- \(p=-\dfrac{5}{3},\ q=-\dfrac{6}{5}\)
- \(p=\dfrac{5}{3},\ q=-\dfrac{6}{5}\)
- \(p=-\dfrac{5}{3},\ q=\dfrac{6}{5}\)
Show Solution
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The Correct Option is D
Solution and Explanation
Step 1: Use the condition for collinear vectors.
If two vectors are collinear, then their corresponding components are proportional.
Therefore, \[ \frac{p}{1} = \frac{-2}{q} = \frac{5}{-3} \] Since \[ \frac{5}{-3}=-\frac{5}{3}, \] we get \[ p=-\frac{5}{3} \]
Step 2: Find the value of \(q\).
Using \[ \frac{-2}{q}=-\frac{5}{3}, \] cross multiplying, \[ -6=-5q \] Hence, \[ q=\frac{6}{5} \]
Step 3: Final conclusion.
Therefore, \[ \boxed{ p=-\frac{5}{3},\quad q=\frac{6}{5} } \]
If two vectors are collinear, then their corresponding components are proportional.
Therefore, \[ \frac{p}{1} = \frac{-2}{q} = \frac{5}{-3} \] Since \[ \frac{5}{-3}=-\frac{5}{3}, \] we get \[ p=-\frac{5}{3} \]
Step 2: Find the value of \(q\).
Using \[ \frac{-2}{q}=-\frac{5}{3}, \] cross multiplying, \[ -6=-5q \] Hence, \[ q=\frac{6}{5} \]
Step 3: Final conclusion.
Therefore, \[ \boxed{ p=-\frac{5}{3},\quad q=\frac{6}{5} } \]
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