Question

Evaluate: $(67,-3,\frac{11}{2}).\left[\right(5,11,3)\times (1,1,3\left)\right]$=...(where $(a,b,c)$ denotes $a\hat{i}+b\hat{j}+c\hat{k}$)

• A. $0$
• B. $1$
• C. $-1$
• D. $2013$

Answer 1

The correct option is D $2013$

$(67,-3,\frac{11}{2}).\left(\right(5,11,3)\times (1,1,3\left)\right)$

$$b=(5,11,3) \times (1,1,3)$

$\Rightarrow \left|\begin{array}{ccc}i& j& k\\ 5& 11& 3\\ 1& 1& 3\end{array}\right|\Rightarrow i(33-3)+j(3-15),k(5-11)i\left(30\right),j(-12),k(-6)$

$(67,-3,\frac{11}{2}).(30,-12,-6)$

$\Rightarrow (67\times 30)+(-3)(-12)+(\frac{11}{2}\times -6)$

$\Rightarrow 2010+36+(-33)$

$\Rightarrow 2010+3$

$\Rightarrow 2013$ option $D$ is correct.