Chapter 10: Q9E (page 564)
Find the resultant vector of \(({\rm{i}} \times {\rm{j}}) \times {\rm{k}}\) using cross product.
The cross product \(({\rm{i}} \times {\rm{j}}) \times {\rm{k}}\) is 0.
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To determine whether the given vectors are orthogonal, parallel, or neither.
(a) For vector\({\rm{a}} = \langle - 5,3,7\rangle \)and\({\rm{b}} = \langle 6, - 8,2\rangle \)
(b) For vector\(a = \langle 4,6\rangle \)and\(b = \langle - 3,2\rangle \)
(c) For vector\({\bf{a}} = - {\bf{i}} + 2{\bf{j}} + 5{\bf{k}}\)and\({\bf{b}} = - 3{\bf{i}} + 4{\bf{j}} - {\bf{k}}\)
(d) For vector\({\bf{a}} = 2{\bf{i}} + 6{\bf{j}} - 4{\bf{k}}\)and\({\bf{b}} = - 3{\bf{i}} - 9{\bf{j}} + 6{\bf{k}}\)
Question: Find the parametric equations for the line through the points \(\left( {0,\frac{1}{2},1} \right)\) and \((2,1, - 3)\) and the symmetric equations for the line through the points \(\left( {0,\frac{1}{2},1} \right)\) and \((2,1, - 3)\).
To find the angle between vectors \(a\) and \(b\) vectors.
Prove the formula\((a \times b) \cdot (c \times d) = \left| {\begin{array}{*{20}{c}}{a \cdot c}&{b \cdot c}\\{a \cdot d}&{b \cdot d}\end{array}} \right|\).
To find the parallel unit vectors to the tangent line of \(y = {x^2}\) parabola.
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