Question:
Given position vectors of A, B, C, D are coplanar, find \(y-x\) for intersection of AB and CD.
Given position vectors of A, B, C, D are coplanar, find \(y-x\) for intersection of AB and CD.
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For coplanar intersection problems, always equate parametric forms component-wise.
Updated On: Jun 22, 2026
- \(2z\)
- \(-4z\)
- \(z\)
- \(-2z\) \bigskip
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The Correct Option is B
Solution and Explanation
Concept:
Use parametric form of lines and solve intersection in vector form.
Step 1: Write position vectors.
Let: \[ A(-1,4,-3),\; B(3,2,-5),\; C(-3,8,-5),\; D(-3,2,1) \]
Step 2: Parametrize AB and CD.
\[ \vec{r}=A+\lambda(B-A) \] \[ \vec{r}=C+\mu(D-C) \]
Step 3: Solve system.
Solving component-wise gives intersection point, and relation: \[ y-x=-4z \] \[ \boxed{(B)} \]
Step 1: Write position vectors.
Let: \[ A(-1,4,-3),\; B(3,2,-5),\; C(-3,8,-5),\; D(-3,2,1) \]
Step 2: Parametrize AB and CD.
\[ \vec{r}=A+\lambda(B-A) \] \[ \vec{r}=C+\mu(D-C) \]
Step 3: Solve system.
Solving component-wise gives intersection point, and relation: \[ y-x=-4z \] \[ \boxed{(B)} \]
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