TS EAMCET · Maths · Three Dimensional Geometry
\(\mathbf{l}, \mathbf{m}, \mathbf{n}\) are three unit vectors in a right handed system and \(L\) is a line through the points \(A, B, C\) whose position vectors are \(p \mathbf{l}+7 \mathbf{m}-6 \mathbf{n}, 2 \mathbf{l}+5 \mathbf{m}-4 \mathbf{n}\) and \(\mathbf{l}+4 \mathbf{m}-3 \mathbf{n}\) respectively. If the equation of the plane containing \(L\) and the points \((-p, p, p+1)\) is \(a x+b y+c z=1\), then \(p(a+b+c)=\)
- A 0
- B \(\frac{-40}{19}\)
- C \(\frac{40}{19}\)
- D -6
Answer & Solution
Correct Answer
(B) \(\frac{-40}{19}\)
Step-by-step Solution
Detailed explanation
Let \(\mathbf{l}, \mathbf{m}, \mathbf{n}\) be \(\hat{\mathbf{i}}, \hat{\mathbf{j}}, \hat{\mathbf{k}}\) \(A(p \hat{\mathbf{i}}+7 \hat{\mathbf{j}}-6 \hat{\mathbf{k}}), B(2 \hat{\mathbf{i}}+5 \hat{\mathbf{j}}-4 \hat{\mathbf{k}})\) and…
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