Chapter 10: Q30RE (page 611)
Determine whether the statement is true or false. If it is true, explain why. If it is false, explain why or give an example that disproves the statement.
The binomial vector is\({\rm{B(t) = N(t)}} \times {\rm{T(t)}}\).
The stated statement is false.
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Find the two unit vectors orthogonal to both \(\langle 3,2,1\rangle \) and \(\langle - 1,1,0\rangle \).
To find a dot product between \({\rm{a}}\) and \({\rm{b}}\).
Find whether the line through the points \(( - 4, - 6,1)\) and \(( - 2,0, - 3)\) is parallel to the line through the points \((10,18,4)\) and \((5,3,14)\) or not.
Find \(|u \times v|\) and determine whether \(u \times v\) is directed into the page or out of the page.
(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 \({R^3}\).
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