Question

The co-ordinates of points $A , B , C , D$ are (a, 2, 1), (1, –1, 1), (2, – 3, 4) and (a+1, a+2, a+3) respectively. If $A B = 5$and $C D = 6$, then $a =$

• A. 2
• B. 3
• C. – 2
• D. – 3

Answer 1

Answer: (D)

– 3

Answer 2

$A B = \sqrt { ( a - 1 ) ^ { 2 } + 3 ^ { 2 } + 0 } = 5$ $\Rightarrow a - 1 = \pm 4$ $\Rightarrow a = - 3,5$

$C D = \sqrt { ( a - 1 ) ^ { 2 } + ( a + 5 ) ^ { 2 } + ( a - 1 ) ^ { 2 } } = 6$

$\Rightarrow a ^ { 2 } - 2 a - 15 = 0 \Rightarrow a = - 3,5$

But common solution of (i) and (ii) is – 3.