JEE Main 2016 · 9 Apr · Shift 1 · Mathematics Q85

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MathematicsSingle correct+4 / -1Question 85 of 90

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 :

parallel to x-axis.

parallel to y-axis.

making an acute angle with the positive direction of x-axis.

making an obtuse angle with the positive direction of x-axis.

Answer and worked solution

Official answer: C

$\vec{AB}\cdot\vec{AC}=(-4,2,p+1)\cdot(2,q-1,-3)=0$ gives $2q-3p=13$ , a line of slope $\frac32>0$ : an acute angle with the x-axis.

Topics:Dot product Equations of a line

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JEE Main 2016 · 9 Apr · Shift 1, Mathematics question 85