Question:
Consider the straight line $\vec{r} = (5\hat{i} + 2\hat{j} - 3\hat{k}) + t(4\hat{i} + 6\hat{j} - 7\hat{k}), \; t \in \mathbb{R}$. Which one of the following points is a point on the straight line?
Consider the straight line $\vec{r} = (5\hat{i} + 2\hat{j} - 3\hat{k}) + t(4\hat{i} + 6\hat{j} - 7\hat{k}), \; t \in \mathbb{R}$. Which one of the following points is a point on the straight line?
Show Hint
Check one coordinate to find $t$, then verify others.
Updated On: Apr 24, 2026
- $(21,24,-31)$
- $(17,20,-22)$
- $(1,-4,5)$
- $(25,32,-38)$
- $(45,66,-36)$
Show Solution
Verified By Collegedunia
The Correct Option is D
Solution and Explanation
Concept:
• Parametric form: $(x,y,z) = (5+4t,\,2+6t,\,-3-7t)$
Step 1: Check option (D)
\[ 25 = 5 + 4t \Rightarrow t = 5 \]
Step 2: Verify other coordinates
\[ y = 2 + 6(5) = 32, \quad z = -3 - 7(5) = -38 \] Matches given point. Final Conclusion:
Option (D)
• Parametric form: $(x,y,z) = (5+4t,\,2+6t,\,-3-7t)$
Step 1: Check option (D)
\[ 25 = 5 + 4t \Rightarrow t = 5 \]
Step 2: Verify other coordinates
\[ y = 2 + 6(5) = 32, \quad z = -3 - 7(5) = -38 \] Matches given point. Final Conclusion:
Option (D)
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