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Magazine Problem 4
For the given vectors \(\mathbf{a}\) and \(\mathbf{b},\) find the cross product \(\mathbf{a} \times \mathbf{b}\). $$\mathbf{a}=\langle 0,-4,1\rangle, \quad \mathbf{b}=\langle 1,1,-2\rangle$$
Problem 4
Two points \(P\) and \(Q\) are given. (a) Plot \(P\) and \(Q .\) (b) Find the distance between \(P\) and \(Q\). $$P(5,0,10), Q(3,-6,7)$$
Problem 4
Find parametric equations for the line that passes through the point \(P\) and is parallel to the vector \(\mathbf{v}\). $$P(0,-5,3), \quad \mathbf{v}=\langle 2,0,-4\rangle$$
Problem 5
For the given vectors \(\mathbf{a}\) and \(\mathbf{b},\) find the cross product \(\mathbf{a} \times \mathbf{b}\). $$\mathbf{a}=\langle 6,-2,8\rangle, \quad \mathbf{b}=\langle- 9,3,-12\rangle$$
Problem 5
Two points \(P\) and \(Q\) are given. (a) Plot \(P\) and \(Q .\) (b) Find the distance between \(P\) and \(Q\). $$P(-2,-1,0), Q(-12,3,0)$$
Problem 5
Find the vector \(\mathbf{v}\) with initial point \(P\) and terminal point \(Q .\) $$P(6,-1,0), Q(0,-3,0)$$
Problem 5
Find parametric equations for the line that passes through the point \(P\) and is parallel to the vector \(\mathbf{v}\). $$P(3,2,1), \quad \mathbf{v}=\langle 0,-4,2\rangle$$
Problem 5
Find \((a) u \cdot v\) and \((b)\) the angle between \(u\) and \(v\) to the nearest degree. $$\mathbf{u}=\langle 2,0\rangle, \quad \mathbf{v}=\langle 1,1\rangle$$
Problem 6
Find parametric equations for the line that passes through the point \(P\) and is parallel to the vector \(\mathbf{v}\). $$P(0,0,0), \quad \mathbf{v}=\langle- 4,3,5\rangle$$
Problem 6
Find \((a) u \cdot v\) and \((b)\) the angle between \(u\) and \(v\) to the nearest degree. $$\mathbf{u}=\mathbf{i}+\sqrt{3} \mathbf{j}, \quad \mathbf{v}=-\sqrt{3} \mathbf{i}+\mathbf{j}$$
