A) passes through three given non-collinear points
B) passes through one point and parallel to two vectors
C) passes through two points and parallel to one vector
D) passes through one point and perpendicular to one vector
Correct Answer: B
Solution :
Given plane is \[\vec{r}=(1-t)\,(3\hat{i}-4\hat{j}+7\hat{k})+t(\hat{i}+\hat{j}-\hat{k})\] \[+s(-2\hat{i}+\hat{j}-\hat{k})\] \[\Rightarrow \] \[\vec{r}=(3\hat{i}-4\hat{j}+7\hat{k})+t(-2\hat{i}+5\hat{j}-8\hat{k})\] \[+s\,(-2\hat{i}+\hat{j}-\hat{k})\] which is of the form \[\vec{r}=\vec{a}+t\,\vec{b}+\,s\,\vec{c}\] and which is the equation of plane passing through a point and parallel to two vectors.
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