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1552test7 - \hfill(6\hbar{3\vskip.75in\item{7 Find the...

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%&amstex \input macro \introdouble \fp{\bf Math 1552 \hfill Test 7 \hfill Name\,\hbar{2}} \jump \item{1.} Find the center and radius of the sphere having the equation $x^2+y^2+z^2-6x-2y+1=0$. \jump \hfill (1) Center:\,\hbar{1}\quad Radius = \,\hbar{1} \vskip .75in \item{2.} Find the vector represented by the directed line segment with initial point $A=(-5,3,5)$ and terminal point $B=(0,-6,2)$. \jump \hfill (2)\,\hbar{1} \bigjump \item{3.} For $\va=<2,-5,3>$ and $\vb=<-4,6,1 >$ find each of the following: \jump \itemitem{(a)} $3\va-5\vb$\,=\,\hbar{2} \hfill (b) $|\va|$\,=\,\hbar{1} \midjump \item{4.} Find a unit vector that has the same direction as the vector $-3\vi+2\vj+5\vk$. \jump \hfill (4)\,\hbar{1.5} \bigjump \item{5.} Find the dot product of $\va=<2,-2,4>$ and $\vb=<1,-7,6>$.\hfill (5)\,\hbar{1} \midjump \item{6.} Determine whether the vectors $\va=-3\vi+2\vj-6\vk$ and $\vb=3\vi-2\vj-6\vk$.are orthogonal by using the dot product. If they are not orthogonal, find the angle between them. \jump
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Unformatted text preview: \hfill (6)\,\hbar{3} \vskip .75in \item{7.} Find the direction angles to the nearest degree for $\va=<2,-6,1>$. \jump \hfill $ alpha=\,\hbar{.5}$\quad $\beta=\,\hbar{.5}$\quad $\gamma =\,\hbar{.5}$ \vskip 1in \item{8.} Find the scalar projection of b onto a and the vector projection of b onto a for $\va=<-3,4>$ and $\vb=<4,5>$. \jump \hfill Scalar projection:\,\hbar{1}\quad Vector Projection:\,\hbar{1} \vskip 1in \item{9.} Find the volume of the parallelepiped determined by the points \item{10.} Find parametric equations and symmetric equations for the line through the points \item{11.} Determine whether the lines are parallel, skew or intersecting. If they intersect, find the point of intersection. \item{12.} Find an equation of the plane through the points \item{13.} Find an equation of the plane through the point and containing the line \item{14.} Determine whether the planes are parallel, perpendicular or neither. Find the angle if neither....
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