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The equation of the plane passing through the line of intersection of the planes \(\vec{r} \cdot(\hat{i}+\hat{j}+\hat{k}…

Q1

The equation of the plane passing through the line of intersection of the planes \(\vec{r} \cdot(\hat{i}+\hat{j}+\hat{k})=1\) and \(\vec{r} \cdot(2 \hat{i}+3 \hat{j}-\hat{k})+4=0\) and parallel to the \(x\)-axis is

[JEE Main 2021, 27 Aug (Shift 2)]

a

\(\vec{r} \cdot(\hat{j}-3 \hat{k})-6=0\)

b

\(\vec{r} \cdot(\hat{i}+3 \hat{k})+6=0\)

c

\(\vec{r} \cdot(\hat{j}-3 \hat{k})+6=0\)

d

\(\vec{r} \cdot(\hat{i}-3 \hat{k})+6=0\)

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