Test Index

KEAM 2012 Math Paper

© examsnet.com

Question : 87 of 120

Marks: +1, -0

If the vectors

3\hat{i}-4\hat{j}-\hat{k}

2\hat{i}+3\hat{j}-6\hat{k}

represent the diagonals of a rhombus, then the length of the side of the rhombus is

15
$15\sqrt{3}$
$\frac{5\sqrt{3}}{2}$
$\frac{15\sqrt{3}}{2}$
$\frac{17\sqrt{3}}{2}$

Solution:

Given,

A C=3 i-4 j-k

and

B D=2 i+3 j-6 k

Let sides of a rhombus be

a

and

b

.

In

\triangle A B C

,

A C=A B+B C

\Rightarrow \;\; 3 i-4 j-k=a+b

̣.....(i)

\therefore \;\; B D=B A+A D

\Rightarrow \;\; 2 i+3 j-6 k=-a+b

......(ii)

On adding Eqs. (i) and (ii), we get

5 i-j-7 k=2 b

\Rightarrow \;\; \left|2 b\right|=\sqrt{5^{2}+1^{2}+7^{2}}

\Rightarrow \;\; \left|b\right|=\;\frac{\sqrt{25+1+49}}{2}

\Rightarrow \;\; \left|b\right|=\;\frac{\sqrt{75}}{2}=\;\frac{5\sqrt{3}}{2}

© examsnet.com

Go to Question:

Prev Question

Next Question