Three Dimensional Geometry
NCERT Exemplar Class 12
CBSE
Grade 12
Question:
Vector equation of line joining points with position vectors $\vec{a}$ and $\vec{b}$ is:
(a) $\vec{r} = (1-\lambda)\vec{a} + \lambda\vec{b}$
(b) $\vec{r} = \vec{a} + \lambda\vec{b}$
(c) $\vec{r} = \vec{a} \times \vec{b}$
(d) $\vec{r} = \lambda(\vec{a} + \vec{b})$
Step-by-Step Solution
r = a + \lambda(b-a) = (1-\lambda)a + \lambda b. [1.0 Mark]
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🎯 Official CBSE Marking Scheme:
Selecting $\vec{r} = (1-\lambda)\vec{a} + \lambda\vec{b}$: 1.0 Mark
Correct Answer: $\vec{r} = (1-\lambda)\vec{a} + \lambda\vec{b}$
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