Question

If $(2,1,3)$ and $(-1,2,4)$ are the extremities of a diagonal of a rhombus then the d.rs of the other diagonal are

• A. $2,3,-9$
• B. $-2,3,-9$
• C. $1,-2,4$
• D. $2,3,1$

Answer 1

Answer: (B)

$-2,3,-9$

$(2,1,3)$ and $(-1,2,4)$ are extremities of a diagonal of a rhombus.
Hence, the direction ratios of that diagonal are equal to $2-(-1),1-2,3-4$.
So, the direction ratios are $3,-1,-1$.
In rhombus the diagonals are perpendicular to each other. Suppose the direction ratios of the other diagonal are $l.m,n$. So, $3l-m-n$ should be equal to zero.
$3l-m-n=0$
Only option B satisfies this condition. Hence the direction ratios are $-2,3,-9$.