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Chapter 17: Problem 1603
two non zero vectors cross product is zero. Then vectors are (a) coplanar (b) equal vectors (c) origin at one point (d) same ending point
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if the angle between \(\underline{a}\) and \(\underline{b}\) is \(\theta\) then \([(|\underline{a} \times \underline{b}|) /(\underline{a} \cdot \underline{b})]=\) (a) \(\tan \theta\) (b) \(-\tan \theta\) (c) \(\cot \theta\) (d) \(-\cot \theta\)
if the vectors \(10 \underline{i}+3 j, 12 \dot{i}-5 j\) and ai \(+11 j\) are collinear then \(\mathrm{a}=\) (a) \(\overline{-8}\) (b) 4 (c) 8 (d) 12
if \(\underline{\mathrm{OA}}=\underline{\mathrm{a}}, \underline{\mathrm{OB}}=\underline{\mathrm{b}}, \underline{\mathrm{OC}}=2 \underline{\mathrm{a}}+3 \underline{\mathrm{b}}, \underline{\mathrm{OD}}=\underline{\mathrm{a}}-2 \underline{\mathrm{b}}\). Length of \(\underline{\mathrm{OA}}\) is three times length of \(\underline{\mathrm{OB}} \& \mathrm{OA}\) is perpendicular to \(\underline{\mathrm{DB}}\) then \((\underline{\mathrm{BD}} \times \underline{\mathrm{AC}}) \cdot(\underline{\mathrm{OD}} \times \underline{\mathrm{OC}})\) is (a) \(7|\underline{\mathrm{a}} \times \underline{\mathrm{b}}|^{2}\) (b) 0 (c) \(7|\underline{a} \times \underline{b}|\) (d) \(42|\underline{\mathrm{a}} \times \underline{\mathrm{b}}|^{2}\)
\(\underline{\mathrm{a}}=\underline{\mathrm{u}}-\underline{\mathrm{v}}, \underline{\mathrm{b}}=\underline{\mathrm{u}}+\underline{\mathrm{v}},|\underline{\mathrm{u}}|=|\underline{\mathrm{u}}|^{2}\) and \(|\underline{\mathrm{u}}|=|\underline{\mathrm{v}}|=2\) find \(|\underline{a} \times \underline{b}|=\) (b) \(\left.\sqrt{[} 4-(\underline{\mathrm{u}} \cdot \underline{\mathrm{v}})^{2}\right]\) (c) \(\sqrt{\left[16-(\underline{\mathrm{u}} \cdot \underline{\mathrm{v}})^{2}\right]}\) (d) \(\sqrt{\left[4-(\underline{\mathrm{u}} \cdot \underline{\mathrm{v}})^{2}\right]}\)
\(\underline{\mathrm{a}}, \underline{\mathrm{b}}\) and \(\underline{\underline{c}}\) are unit vectors, \(\underline{\mathrm{a}}+\underline{\mathrm{b}}+\underline{\mathrm{c}}=\underline{0}\) then \(\underline{\mathrm{a}} \cdot \underline{\mathrm{b}}+\underline{\mathrm{b}} \cdot \underline{\mathrm{c}}+\underline{\mathrm{c}} \cdot \underline{\mathrm{a}}=\) (a) 1 (b) 3 (c) \(-(3 / 2)\) (d) none of these
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