JEE Mains · Maths · STD 12 - 11. three dimension geometry
The equation of the plane passing through the line of intersection of the planes \(\vec{r} .(\hat{i}+\hat{j}+\hat{k})=1\) and \(\vec{r} \cdot(2 \hat{\mathrm{i}}+3 \hat{\mathrm{j}}-\hat{\mathrm{k}})+4=0\) and parallel to the \(\mathrm{x}\)-axis is:
- A \(\vec{r} \cdot(\hat{j}-3 \hat{k})+6=0\)
- B \(\overrightarrow{\mathrm{r}} \cdot(\hat{\mathrm{i}}+3 \hat{\mathrm{k}})+6=0\)
- C \(\vec{r} \cdot(\hat{i}-3 \hat{k})+6=0\)
- D \(\vec{r} \cdot(\hat{j}-3 \hat{k})-6=0\)
Answer & Solution
Correct Answer
(A) \(\vec{r} \cdot(\hat{j}-3 \hat{k})+6=0\)
Step-by-step Solution
Detailed explanation
Equation of planes are \(\overrightarrow{\mathrm{r}} \cdot(\hat{\mathrm{i}}+\hat{\mathrm{j}}+\hat{\mathrm{k}})-1=0 \Rightarrow \mathrm{x}+\mathrm{y}+\mathrm{z}-1=0\) and…
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