# 6 5 pts suppose v 3 2 1 and w 124 then v w 7 5 pts

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_________________________________________________________________ 6. (5 pts.) Suppose v = <-3,-2, 1> and w = <-1,2,4>. Then v w = _________________________________________________________________ 7. (5 pts.) Suppose v = <-3,-2, 1> and w = <-2,2,1>. Then v × w = _________________________________________________________________ 8. (5 pts.) Suppose v = <-3,-2, 1> and w = <-1,2,4>. Then proj w ( v ) = , and the component of v perpendicular to w is w 2 = .

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TEST1/MAC2313 Page 3 of 5 _________________________________________________________________ 9. (5 pts.) Suppose v = <-3,-2, 1> and w = <-2,2,1>. If α , β , and γ are the direction angles of w , then cos( α ) = , cos( β ) = ,and cos( γ ) = . _________________________________________________________________ 10. (5 pts.) Suppose v = <-3,-2, 1> and w = <-1,2,4>. What is the exact value of the angle θ between v and w ?? θ = _________________________________________________________________ 11. (5 pts.) Write a point-normal equation for the plane perpendicular to v = <-3,-2,1> and containing the point (3 π ,2 π , π ). _________________________________________________________________ 12. (5 pts.) Write an equation for the plane passing through the point (4,-5, 6) and perpendicular to the line defined by the vector equation <x,y,z> = <4e,25,2 π > + t<2,-3,-3>.
TEST1/MAC2313 Page 4 of 5 _________________________________________________________________ 13. (5 pts.) Find the exact value of the acute angle θ of intersection of the two planes defined by the two equations x - 2y = -55 and 3y - 4z = 75. θ = _________________________________________________________________ 14. (5 pts.) Write an equation for the plane which contains the line defined by <x,y,z> = <1,2,3> + t<3, -2, 1> and is perpendicular to the plane defined by x - 2y + z = 0. _________________________________________________________________ 15. (5 pts.) What is the radius of the sphere centered at (1, 0, 0) and tangent to the plane defined by x + 2y + z = 10?

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