Search any question & find its solution
Question:
Answered & Verified by Expert
If $[\bar{a} \bar{b} \bar{c}] \neq 0$, then $\frac{[\bar{a}+\bar{b} \quad \bar{b}+\bar{c} \quad \bar{c}+\bar{a}]}{[\bar{b} \bar{c} \bar{a}]}=$
Options:
Solution:
1404 Upvotes
Verified Answer
The correct answer is:
2
(D)
$\left[\begin{array}{lll}\bar{a}+\bar{b} & \bar{b}+\bar{c} & \bar{c}+\bar{a}\end{array}\right]$
$=(\bar{a}+\bar{b}) \cdot[(\bar{b}+\bar{c}) \times(\bar{c}+\bar{a})]$
$=(\bar{a}+\bar{b}) \cdot[(\bar{b} \times \bar{c})+(\bar{b} \times \bar{a})+(\bar{c} \times \bar{c})+(\bar{c} \times \bar{a})]$
$=[\bar{a} \cdot(\bar{b} \times \bar{c})]+[\bar{a} \cdot(\bar{b} \times \bar{a})]+[\bar{a} \cdot(\bar{c} \times \bar{a})]+[\bar{b} \cdot(\bar{b} \times \bar{c})]+[\bar{b} \cdot(\bar{b} \times \bar{a})]+[\bar{b} \cdot(\bar{c} \times \bar{a})]$
$=[\bar{a} \cdot(\bar{b} \times \bar{c})]+[\bar{b} \cdot(\bar{c} \times \bar{a})]$
$=2[\bar{a} \cdot(\bar{b} \times \bar{c})] \quad=2\left[\begin{array}{lll}\bar{a} & \bar{b} & \bar{c}\end{array}\right]$
Hence give expression $=\frac{2[\bar{a} \bar{b} \bar{c}]}{[\bar{a} \bar{b} \bar{c}]}=2$
$\left[\begin{array}{lll}\bar{a}+\bar{b} & \bar{b}+\bar{c} & \bar{c}+\bar{a}\end{array}\right]$
$=(\bar{a}+\bar{b}) \cdot[(\bar{b}+\bar{c}) \times(\bar{c}+\bar{a})]$
$=(\bar{a}+\bar{b}) \cdot[(\bar{b} \times \bar{c})+(\bar{b} \times \bar{a})+(\bar{c} \times \bar{c})+(\bar{c} \times \bar{a})]$
$=[\bar{a} \cdot(\bar{b} \times \bar{c})]+[\bar{a} \cdot(\bar{b} \times \bar{a})]+[\bar{a} \cdot(\bar{c} \times \bar{a})]+[\bar{b} \cdot(\bar{b} \times \bar{c})]+[\bar{b} \cdot(\bar{b} \times \bar{a})]+[\bar{b} \cdot(\bar{c} \times \bar{a})]$
$=[\bar{a} \cdot(\bar{b} \times \bar{c})]+[\bar{b} \cdot(\bar{c} \times \bar{a})]$
$=2[\bar{a} \cdot(\bar{b} \times \bar{c})] \quad=2\left[\begin{array}{lll}\bar{a} & \bar{b} & \bar{c}\end{array}\right]$
Hence give expression $=\frac{2[\bar{a} \bar{b} \bar{c}]}{[\bar{a} \bar{b} \bar{c}]}=2$
Looking for more such questions to practice?
Download the MARKS App - The ultimate prep app for IIT JEE & NEET with chapter-wise PYQs, revision notes, formula sheets, custom tests & much more.