# Second Year Math Vectors

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$11. Find the scalar (area) of the triangle \mathrm{ABC} where \mathrm{A} \mathrm{B} \mathrm{C} are the ooints;(ii) A:(110) B:(2-12) C:(000) .$

$Can the magnitude of a vector have a negative value?$

7. Find the direction cosines of \overrightarrow{A B} in each of the five cases of question 4 . and then write \overline{A B} in the form\[r=r(\cos \alpha i+\cos \beta j+\cos \gamma k)\](iii) A\left(-\frac{1}{3} \frac{5}{3} 2\right) ; B\left(1-2 \frac{2}{3}\right)

$5. If \underline{v} is a vector for which \underline{v} \underline{\underline{i}}=0 \underline{v} \cdot \underline{j}=0 \underline{v} \cdot \underline{k}=0 find \underline{v} .$

$7. If \underline{a}+\underline{b}+\underline{c}=0 then prove that \underline{a} \times \underline{b}=\underline{b} \times \underline{c}=\underline{c} \times \underline{a}$

$8. Prove that: \sin (\alpha-\beta)=\sin \alpha \cos \beta+\cos \alpha \sin \beta .$