Question
Download Solution PDFयदि बिंदु (1, 3, -2), (2, λ, 1) और (3, 4, -1) एक-दूसरे के समतलीय हैं, तो λ का मान क्या है?
Answer (Detailed Solution Below)
Detailed Solution
Download Solution PDFसंकल्पना:
बिंदु (x1, y1, z1), (x2, y2, z2) और (x3, y3, z3) के समतलीय होने के लिए
\(\rm \begin{vmatrix} x_1 & y_1 &z_1 \\ x_2& y_2& z_2 \\ x_3& y_3& z_3 \end{vmatrix} = 0\)
गणना:
दिए गए बिंदु (1, 3, -2), (2, λ, 1) और (3, 4, -1) हैं।
तल का समीकरण निम्न होगा
\(\rm \begin{vmatrix} 1 &3 &-2\\ 2& λ& 1\\ 3&4& -1 \end{vmatrix} = 0\)
⇒ 1(-λ - 4) - 3(-2 - 3) + (-2)(8 - 3λ) = 0
⇒ 5λ - 4 + 15 - 16 = 0
⇒ 5λ = 5
⇒ λ = 1
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