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Q.The line r⃗=i^+j^+k^+λ(2i^+3j^+6k^)\vec{r} = \hat{i} + \hat{j} + \hat{k} + \lambda (2\hat{i} + 3\hat{j} + 6\hat{k}) is parallel to the plane

a
r⃗⋅(i^−j^+k^)=0\vec{r} \cdot (\hat{i} - \hat{j} + \hat{k}) = 0
b
r⃗⋅(i^+j^−k^)=0\vec{r} \cdot (\hat{i} + \hat{j} - \hat{k}) = 0
c
r⃗⋅(3i^−j^+k^)=0\vec{r} \cdot (3\hat{i} - \hat{j} + \hat{k}) = 0
d
r⃗⋅(i^−3j^+k^)=0\vec{r} \cdot (\hat{i} - 3\hat{j} + \hat{k}) = 0

Correct Answer: Option A

The correct solution involves applying the fundamental concept to derive the final value step by step...

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