91Ó°ÊÓ

Find (a) \(\mathbf{u} \cdot \mathbf{v}\) and \((\mathbf{b})\) the angle between \(\mathbf{u}\) and \(\mathbf{v}\) to the nearest degree. $$\mathbf{u}=2 \mathbf{i}+\mathbf{j}, \quad \mathbf{v}=3 \mathbf{i}-2 \mathbf{j}$$

Two vectors \(u\) and \(v\) are given. (a) Find a vector orthogonal (perpendicular) to both \(\mathbf{u}\) and \(\mathbf{v}\). (b) Find a unit vector orthogonal (perpendicular) to both \(\mathbf{u}\) $$\mathbf{u}=\langle 2,5,3\rangle, \quad \mathbf{v}=\langle 3,-2,-1\rangle$$

Find (a) \(\mathbf{u} \cdot \mathbf{v}\) and \((\mathbf{b})\) the angle between \(\mathbf{u}\) and \(\mathbf{v}\) to the nearest degree. $$\mathbf{u}=-5 \mathbf{j}, \quad \mathbf{v}=-\mathbf{i}-\sqrt{3} \mathbf{j}$$

Find the magnitude of the given vector. $$\langle- 2,1,2\rangle$$

Two vectors \(u\) and \(v\) are given. (a) Find a vector orthogonal (perpendicular) to both \(\mathbf{u}\) and \(\mathbf{v}\). (b) Find a unit vector orthogonal (perpendicular) to both \(\mathbf{u}\) $$\mathbf{u}=\frac{1}{2} \mathbf{i}-\mathbf{j}+\frac{2}{3} \mathbf{k}, \quad \mathbf{v}=6 \mathbf{i}-12 \mathbf{j}-6 \mathbf{k}$$

Equation of a Sphere Find an equation of a sphere with the given radius \(r\) and center \(C\). $$r=5 ; \quad C(2,-5,3)$$

Two vectors \(u\) and \(v\) are given. (a) Find a vector orthogonal (perpendicular) to both \(\mathbf{u}\) and \(\mathbf{v}\). (b) Find a unit vector orthogonal (perpendicular) to both \(\mathbf{u}\) $$\mathbf{u}=3 \mathbf{j}+5 \mathbf{k}, \quad \mathbf{v}=-\mathbf{i}+2 \mathbf{k}$$

Find the magnitude of the given vector. $$\langle 5,0,-12\rangle$$

Equation of a Sphere Find an equation of a sphere with the given radius \(r\) and center \(C\). $$r=3 ; \quad C(-1,4,-7)$$

Solve the given equation. $$\cos \theta=0.32$$