TS EAMCET · Maths · Three Dimensional Geometry
A point lying on the plane that passes through the points \(\hat{\mathbf{i}}-\hat{\mathbf{j}}+\hat{\mathbf{k}}, \hat{\mathbf{i}}-2 \hat{\mathbf{j}}+3 \hat{\mathbf{k}}\) and \(\hat{\mathbf{i}}+2 \hat{\mathbf{j}}-3 \hat{\mathbf{k}}\) is
- A \(-\hat{\mathbf{i}}+2 \hat{\mathbf{j}}-3 \hat{\mathbf{k}}\)
- B \(-\hat{\mathbf{i}}+\hat{\mathbf{j}}-\hat{\mathbf{k}}\)
- C \(\hat{\mathbf{i}}+\hat{\mathbf{j}}-\hat{\mathbf{k}}\)
- D \(4 \hat{\mathbf{i}}+2 \hat{\mathbf{j}}+3 \hat{\mathbf{k}}\)
Answer & Solution
Correct Answer
(C) \(\hat{\mathbf{i}}+\hat{\mathbf{j}}-\hat{\mathbf{k}}\)
Step-by-step Solution
Detailed explanation
Equation of plane passing through 3 given point is \[ \left|\begin{array}{ccc} x-x_1 & y-y_1 & z-z_1 \\ x_2-x_1 & y_2-y_1 & z_2-z_1 \\ x_3-x_1 & y_3-y_1 & z_3-z_1 \end{array}\right|=0 \] So,…
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