TS EAMCET · Maths · Three Dimensional Geometry
The equation of the plane passing through the points with position vectors \(A(2 \hat{\mathbf{i}}+6 \hat{\mathbf{j}}-6 \hat{\mathbf{k}})\), \(B(-3 \hat{\mathbf{i}}+10 \hat{\mathbf{j}}-9 \hat{\mathbf{k}})\) and \(C(-5 \hat{\mathbf{i}}-6 \hat{\mathbf{k}})\) is
- A \(\mathbf{r} \cdot(2 \hat{\mathbf{i}}-\hat{\mathbf{j}}-2 \hat{\mathbf{k}})=2\)
- B \(\mathbf{r} \cdot(\hat{\mathbf{i}}-2 \hat{\mathbf{j}}-\hat{\mathbf{k}})=1\)
- C \(\mathbf{r} \cdot(2 \hat{\mathbf{i}}+\hat{\mathbf{j}}-2 \hat{\mathbf{k}})=3\)
- D \(\mathbf{r} \cdot(\hat{\mathbf{i}}+2 \hat{\mathbf{j}}-2 \hat{\mathbf{k}})=3\)
Answer & Solution
Correct Answer
(A) \(\mathbf{r} \cdot(2 \hat{\mathbf{i}}-\hat{\mathbf{j}}-2 \hat{\mathbf{k}})=2\)
Step-by-step Solution
Detailed explanation
Equation of plane passing through any three given point is \[ \left|\begin{array}{lll} x-x_1 & y-y_1 & z-z_1 \\ x_2-x_1 & y_2-y_1 & z_2-z_1 \\ x_3-x_1 & y_3-y_1 & z_3-z_1 \end{array}\right|=0 \] Points are \((-2,6,-6),(-3,10,-9)\) and \((-5,0,-6)\)…
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