JEE Mains · Maths · STD 12 - 11. three dimension geometry
The length of the projection of the line segment joining the point \(\left( {5, - 1,4} \right)\) and \(\left( {4, - 1,3} \right)\) on the plane \(x + y + z = 7\) is :
- A \(\frac{2}{3}\)
- B \(\frac{1}{3}\)
- C \(\sqrt {\frac{2}{3}} \)
- D \(\frac{2}{{\sqrt 3 }}\)
Answer & Solution
Correct Answer
(C) \(\sqrt {\frac{2}{3}} \)
Step-by-step Solution
Detailed explanation
\(A C=\overrightarrow{A B} \cdot \hat{A C}=(\hat{i}+\hat{k}) \cdot \frac{(\hat{i}+\hat{j}+\hat{k})}{\sqrt{3}}=\frac{2}{\sqrt{3}}\) Now, \(A^{\prime} B^{\prime}=B C=\sqrt{A B^{2}-A C^{2}}=\sqrt{2-\frac{4}{3}}=\sqrt{\frac{2}{3}}\) Length of projection \(=\sqrt{\frac{2}{3}}\)
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