Chapter 10: Q2RE (page 611)
For any vectors \({\rm{u}}\) and \({\rm{v}}\) in\({{\rm{V}}_{\rm{3}}}{\rm{,|u + v| = |u| + |v|}}\).
The statement is false.
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(a) Find whether the statement (Two lines parallel to a third line are parallel) is true or false in \({R^3}\).
(b) Find whether the statement (Two lines perpendicular to a third line are parallel) is true or false in \({R^3}\).
(c) Find whether the statement (Two planes parallel to a third plane are parallel) is true or false in \({R^3}\).
(d) Find whether the statement (Two planes perpendicular to a third plane are parallel) is true or false in \({R^3}\).
(e) Find whether the statement (Two lines parallel to a plane are parallel) is true or false in \({R^3}\).
(f) Find whether the statement (Two lines perpendicular to a plane are parallel) is true or false in \({R^3}\).
(g) Find whether the statement (Two planes parallel to a line are parallel) is true or false in \({R^3}\).
(h) Find whether the statement (Two planes perpendicular to a line are parallel) is true or false in \({R^3}\).
(i) Find whether the statement (Two planes either intersect or are parallel) is true or false in \({R^3}\).
(j) Find whether the statement (Two line either intersect or are parallel) is true or false in \({R^3}\).
(k) Find whether the statement (A plane and line either intersect or are parallel) is true or false in \({R^3}\).
To determine whether the triangle with vertices is right-angled.
To d\({\bf{b}} = \left\langle {{b_1},{b_2},{b_3}} \right\rangle \)escribe all set of points for condition \(\left| {{\bf{r}} - {{\bf{r}}_0}} \right| = 1\).
Find the parametric equations for the line through the point \((2,1,0)\) and perpendicular to both vectors \(i + j\) and \(j + k\) and the symmetric equations for the line through the point \((2,1,0)\) and perpendicular to both vectors \(i + j\) and \(j + k\).
To determine the dot product between two vector \({\rm{a}}\) and \({\rm{b}}\).
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