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Standard XII

Mathematics

Direction Ratios

Points A 6,-1...

Question

Points $A (6, - 10, 3), B (5, p, 6) and C (11, - 5, q)$ form a triangle in which median $A D$ makes equal angle with the positive $x, y and z$ axes, then the value of $p + q$ is

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Solution

The correct option is C $- 7$
Coordinates of $D (8, \frac{p - 5}{2}, \frac{6 + q}{2})$
$- - \to A D = (2 + \frac{p + 15}{2}, \frac{q}{2})$
$∵ A D$ makes equal angle with the positive coordinate axes
$∴ 2 = \frac{p + 15}{2} \Rightarrow p = - 11, 2 = \frac{q}{2} \Rightarrow q = 4$

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Points A(6,−10,3), B(5,p,6) and C(11,−5,q) form a triangle in which median AD makes equal angle with the positive x,y and z axes, then the value of p+q is

The correct option is C −7Coordinates of D(8,p−52,6+q2) −−→AD=(2+p+152,q2) ∵AD makes equal angle with the positive coordinate axes ∴2=p+152⇒p=−11,2=q2⇒q=4

Points $A (6, - 10, 3), B (5, p, 6) and C (11, - 5, q)$ form a triangle in which median $A D$ makes equal angle with the positive $x, y and z$ axes, then the value of $p + q$ is

The correct option is C $- 7$
Coordinates of $D (8, \frac{p - 5}{2}, \frac{6 + q}{2})$
$- - \to A D = (2 + \frac{p + 15}{2}, \frac{q}{2})$
$∵ A D$ makes equal angle with the positive coordinate axes
$∴ 2 = \frac{p + 15}{2} \Rightarrow p = - 11, 2 = \frac{q}{2} \Rightarrow q = 4$