JEE Mains · Maths · STD 12 - 10. vector algebra
Let \(\mathrm{A}(x, y, z)\) be a point in \(x y\)-plane, which is equidistant from three points \((0,3,2),(2,0,3)\) and ( \(0,0,1\) ).
Let \(\mathrm{B}=(1,4,-1)\) and \(\mathrm{C}=(2,0,-2)\). Then among the statements
(S1) : \(\triangle \mathrm{ABC}\) is an isosceles right angled triangle, and
(S2) : the area of \(\triangle \mathrm{ABC}\) is \(\frac{9 \sqrt{2}}{2}\),
- A both are true
- B only (S2) is true
- C only (S1) is true
- D both are false
Answer & Solution
Correct Answer
(C) only (S1) is true
Step-by-step Solution
Detailed explanation
\begin{aligned} & \mathrm{A}(\mathrm{x}, \mathrm{y}, \mathrm{z}) \text { Let } \mathrm{P}(0,3,2), \mathrm{Q}(2,0,3), \mathrm{R}(0,0,1) \\ & \mathrm{AP}=\mathrm{AQ}=\mathrm{AR} \\ &…
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