In a triangle ABC, right angle at vertex A, if the position vectors of A,B and C are respectively 3i^+ j^- k^, -i^+3j^+pk^ and 5i^+qj^-4k^ , then the…

Question

In a triangle ABC, right angle at vertex A, if the position vectors of A,B and C are respectively 3i^+ j^- k^, -i^+3j^+pk^ and 5i^+qj^-4k^ , then the point p,q lies on a line:

MARKS Content Team · Accepted Answer

Correct answer: (D) Making an acute angle with the positive direction of x-axis. AB→= -4i^+2j^+p+1k^ AC→= 2i^+q-1j^-3k^ AB→⊥AC→ ⇒ AB→ · AC→=0 -8+2q-1-3p+1=0 3p-2q+13=0 p,q lies on 3x-2y+13=0 Slope =3/2 ∴ The required line makes an acute angle with the positive direction of x-axis.

In a triangle $A B C$ , right angle at 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:

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