Question

If the co-ordinates of the points $A , B , C$ be $( - 1,3,2 ) , ( 2,3,5 )$ and (3, 5,–2) respectively, then $\angle A =$

• A. $0 ^ { \circ }$
• B. $45 ^ { \circ }$
• C. $60 ^ { \circ }$
• D. $90 ^ { \circ }$

Answer 1

Answer: (D)

$90 ^ { \circ }$

Answer 2

Equation of AB is $\frac { x + 1 } { 3 } = \frac { y - 3 } { 0 } = \frac { z - 2 } { 3 }$ …..(i)

and that of AC is $\frac { x + 1 } { 4 } = \frac { y - 3 } { 2 } = \frac { z - 2 } { - 4 }$ .....(ii)

Hence $\angle A = \cos ^ { - 1 } \left( \frac { 12 + 0 - 12 } { \sqrt { 9 + 9 } \sqrt { 16 + 4 + 16 } } \right) = 90 ^ { \circ }$.