CUET · MATHS · PYQ PAPER 2023
\(\vec{n}\) is a vector of magnitude \(2 \sqrt{3}\) such that it makes equal angles with coordinate axes. The vector equation of the plane passing through (1, -1, 2) and perpendicular to \(\vec{n}\) is:
- A \(\vec{r} \cdot(\hat{i}+\hat{j}+\hat{k})=2\)
- B \(\vec{r} \cdot(\hat{i}+\hat{j}+\hat{k})=2 \sqrt{3}\)
- C \(\vec{r} \cdot(2 \hat{i}-\hat{j}+\hat{k})=2\)
- D \(\vec{r} \cdot(2 \hat{i}-\hat{j}+\hat{k})=\sqrt{3}\)
Answer & Solution
Correct Answer
(A) \(\vec{r} \cdot(\hat{i}+\hat{j}+\hat{k})=2\)
Step-by-step Solution
Detailed explanation
Let the direction cosines of \(\vec{n}\) be \(\cos\alpha, \cos\beta, \cos\gamma\). Since \(\vec{n}\) makes equal angles with coordinate axes, \(\cos\alpha = \cos\beta = \cos\gamma\).…
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