Chapter 10: Q22E (page 589)
Match the parametric equations with the graphs (labeled I–VI). Give reasons for your choices. 22.\(x = co{s^2}t,\;y = si{n^2}t,\;z = t\).
The answer is graph no III
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Find a vector equation for a line through the point\((6, - 5,2)\)and parallel to the vector\(\left\langle {1,3, - \frac{2}{3}} \right\rangle \)and the parametric equations for a line through the point\((6, - 5,2)\)and parallel to the vector\(\left\langle {1,3, - \frac{2}{3}} \right\rangle \).
To describe the set of all points for condition \(\left| {{\bf{r}} - {{\bf{r}}_1}} \right| + \left| {{\bf{r}} - {{\bf{r}}_2}} \right| = k\).
(a) Determine whether expression \(a \cdot (b \times c)\) is meaningful or meaningless.
(b) Determine whether expression \(a \times (b \cdot c)\) is meaningful or meaningless.
(c) Determine whether expression \({\rm{a}} \times ({\rm{b}} \times {\rm{c}})\) is meaningful or meaningless.
(d) Determine whether expression \(a \cdot (b \cdot c)\) is meaningful or meaningless.
(e) Determine whether expression \((a \cdot b) \times (c \cdot d)\) is meaningful or meaningless.
(f) Determine whether expression \((a \times b) \cdot (c \times d)\) is meaningful or meaningless.
To determine
To verify: The vectors \(u = i + 5j - 2k,v = 3i - j\) and \(w = 5i + 9j - 4k\) are coplanar.
Prove the property\((a \times b) = - b \times a\).
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