JEE Mains · Maths · STD 12 - 10. vector algebra
In a triangle \(ABC,\) right angled at the vertex \(A,\) if the position vectors of \(A, B\) and \(C\) are respectively \(3\hat i\, + \hat j\, - \hat k,\,\, - \hat i\, + 3\hat j\, + p\hat k\) and \(5\hat i\, + q\hat j\, - 4\hat k,\,\) then the point \((p, q)\) lies on a line
- A making an obtuse angle with the positive direction of \(x-\) axis
- B parallel to \(x-\) axis
- C parallel to \(y -\) axis
- D making an acute angle with the positive direction of \(x-\) axis
Answer & Solution
Correct Answer
(D) making an acute angle with the positive direction of \(x-\) axis
Step-by-step Solution
Detailed explanation
\(\overline{A B}=-4 \hat{i}+2 \hat{j}+(p+1) \hat{k}\) \(\overline {AC} = 2\hat i + (q - 1)\hat j - 3\hat k\) \(\overline {AB} \bot \overline {AC} \) \( \Rightarrow \overline {AB} .\overline {AC} = 0\) \(-8+2(q-1)-3(p+1)=0\) \(3 p-2 q+13=0\) \((p, q)\) lies on \(3 x-2 y+13=0\)…
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