91Ó°ÊÓ

Using the Cross Product In Exercises \(29-36,\) find a unit vector that is orthogonal to both \(u\) and v. $$\mathbf{u}=\langle 2,-3,4\rangle$$ $$\mathbf{v}=\langle 0,-1,1\rangle$$

Finding the Distance Between Two Points in Space In Exercises \(27-36,\) tind the distance between the points. $$(3,2,5),(7,4,8)$$

Finding an Equation of a Plane in Three-Space In Exercises \(27 - 30\) , find the general form of the equation of the plane passing through the three points. $$ ( 2,3 , - 2 ) , ( 3,4,2 ) , ( 1 , - 1,0 ) $$

Finding the Magnitude of a Vector ,find the magnitude of \(v\) . $$\mathbf{v}=\mathbf{i}+3 \mathbf{j}-\mathbf{k}$$

Finding the Magnitude of a Vector ,find the magnitude of \(v\) . $$\mathbf{v}=-\mathbf{i}-4 \mathbf{j}+3 \mathbf{k}$$

Finding an Equation of a Plane in Three-Space In Exercises \(27 - 30\) , find the general form of the equation of the plane passing through the three points. $$ ( 5 , - 1,4 ) , ( 1 , - 1,2 ) , ( 2,1 , - 3 ) $$

Using the Cross Product In Exercises \(29-36,\) find a unit vector that is orthogonal to both \(u\) and v. $$\mathbf{u}=\langle 2,-1,3\rangle$$ $$\mathbf{v}=\langle 1,0,-2\rangle$$

Finding the Distance Between Two Points in Space In Exercises \(27-36,\) tind the distance between the points. $$(4,1,5),(8,2,6)$$

Finding the Distance Between Two Points in Space In Exercises \(27-36,\) tind the distance between the points. $$(-1,4,-2),(6,0,-9)$$

Finding the Magnitude of a Vector ,find the magnitude of \(v\) . Initial point: \((1,-3,4) ;\) terminal point: \((1,0,-1)\)