Question:
The points with position vectors \(60\hat{i}+3\hat{j}, 40\hat{i}-8\hat{j}, a\hat{i}-52\hat{j}\) are collinear if
The points with position vectors \(60\hat{i}+3\hat{j}, 40\hat{i}-8\hat{j}, a\hat{i}-52\hat{j}\) are collinear if
Show Hint
Equal slopes ⇒ collinear points.
Updated On: Apr 30, 2026
- \(a=-10\)
- \(a=40\)
- \(a=20\)
- \(a=10\)
- \(a=-40\)
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The Correct Option is C
Solution and Explanation
Concept:
Points are collinear if slopes are equal.
Step 1: Write coordinates. \[ A(60,3), B(40,-8), C(a,-52) \]
Step 2: Slope AB. \[ \frac{-8-3}{40-60} = \frac{-11}{-20} = \frac{11}{20} \]
Step 3: Slope BC. \[ \frac{-52+8}{a-40} = \frac{-44}{a-40} \]
Step 4: Equate slopes. \[ \frac{11}{20} = \frac{-44}{a-40} \] \[ 11(a-40) = -880 \] \[ a-40 = -80 \] \[ a = -40 \]
Step 1: Write coordinates. \[ A(60,3), B(40,-8), C(a,-52) \]
Step 2: Slope AB. \[ \frac{-8-3}{40-60} = \frac{-11}{-20} = \frac{11}{20} \]
Step 3: Slope BC. \[ \frac{-52+8}{a-40} = \frac{-44}{a-40} \]
Step 4: Equate slopes. \[ \frac{11}{20} = \frac{-44}{a-40} \] \[ 11(a-40) = -880 \] \[ a-40 = -80 \] \[ a = -40 \]
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