Question
If $\vec{\text{a}}$ and $\vec{\text{b}}$ are two vectors such that $\big|\vec{\text{a}}\big|=4,\big|\vec{\text{b}}\big|=3$ and $\vec{\text{a}}.\vec{\text{b}}=6,$ find the angle between $\vec{\text{a}}$ and $\vec{\text{b}}$.
Given that
$\vec{\text{a}}.\vec{\text{b}}=6$
$\Rightarrow\big|\vec{\text{a}}\big|\big|\vec{\text{b}}\big|\cos\theta=6$
$\Rightarrow(4)(3)\cos\theta=6$
$\Rightarrow12\cos\theta=6$
$\Rightarrow\cos\theta=\frac{6}{12}=\frac{1}{2}$
$\Rightarrow\theta=\cos^{-1}\big(\frac{1}{2}\big)=\frac{\pi}{3}$
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The number of attempts made in three villages X, Y and Z are given below:
| (i) | (ii) | (iii) | |
| X | 400 | 300 | 100 |
| Y | 300 | 250 | 75 |
| Z | 500 | 400 | 150 |
Find the total cost incurred by the organisation for three villages separately, using matrices.