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Magazine Problem 8
Find parametric equations for the line that passes through the point \(P\) and is parallel to the vector \(\mathbf{v} .\) $$ P(1,1,1), \quad \mathbf{v}=\mathbf{i}-\mathbf{j}+\mathbf{k} $$
Problem 8
\(7-10\) . Describe and sketch the surface represented by the given equation. \(y=-2\)
Problem 8
For the given vectors a and b, find the cross product \(\mathbf{a} \times \mathbf{b}\). $$ \mathbf{a}=3 \mathbf{i}-\mathbf{j}, \quad \mathbf{b}=-3 \mathbf{j}+\mathbf{k} $$
Problem 9
Find (a) \(\mathbf{u} \cdot \mathbf{v}\) and (b) the angle between \(\mathbf{u}\) and \(\mathbf{v}\) to the nearest degree. $$ \mathbf{u}=\langle 3,-2\rangle, \quad \mathbf{v}=\langle 1,2\rangle $$
Problem 9
If the vector \(\mathbf{v}\) has initial point \(P,\) what is its terminal point? $$ \mathbf{v}=\langle- 2,0,2\rangle, P(3,0,-3) $$
Problem 9
Two vectors a and b are given. (a) Find a vector perpendicular to both a and b. (b) Find a unit vector perpendicular to both a and b. $$ \mathbf{a}=\langle 1,1,-1\rangle, \quad \mathbf{b}=\langle- 1,1,-1\rangle $$
Problem 9
Find parametric equations for the line that passes through the points \(P\) and \(Q .\) $$ P(1,-3,2), \quad Q(2,1,-1) $$
Problem 9
\(7-10\) . Describe and sketch the surface represented by the given equation. \(z=8\)
Problem 10
Find (a) \(\mathbf{u} \cdot \mathbf{v}\) and (b) the angle between \(\mathbf{u}\) and \(\mathbf{v}\) to the nearest degree. $$ \mathbf{u}=2 \mathbf{i}+\mathbf{j}, \quad \mathbf{v}=3 \mathbf{i}-2 \mathbf{j} $$
Problem 10
Two vectors a and b are given. (a) Find a vector perpendicular to both a and b. (b) Find a unit vector perpendicular to both a and b. $$ \mathbf{a}=\langle 2,5,3\rangle, \quad \mathbf{b}=\langle 3,-2,-1\rangle $$
