Is four fifths of the way from p 2 3 to q 487 6 5 pts

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) is four-fifths of the way from P = (-2,-3) to Q = (48,7) ?? ______________________________________________________________________ 6. (5 pts.) Suppose v = <-3,-2, 1> and w = <-1,1,1>. Then v w = ______________________________________________________________________ 7. (5 pts.) Suppose v = <-3,-2, 1> and w = <-1,1,1>. Then v × w = ______________________________________________________________________ 8. (5 pts.) Suppose v = <-3,-2, 1> and w = <-1,1,1>. 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,-4, 5> and w = <-1,1,1>. If α , β , and γ are the direction angles of v , then cos( α ) = , cos( β ) = ,and cos( γ ) = . ______________________________________________________________________ 10. (5 pts.) Suppose v = <-3,-2, 1> and w = <-1,1,1>. 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 (-1,2,-3). ______________________________________________________________________ 12. (5 pts.) Which point on the line defined the vector equation <x,y,z> = <1,1,1> + t<2,-1,-1> is nearest the point, (0,-1,0)?
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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 - 3y = -5 and 2y - 4z = 7. 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.) Obtain an equation for the plane tangent to the sphere defined by ( x 1) 2 ( y 2) 2 ( z 3) 2 9 at the point (2, -4, 5), which is actually on the sphere.
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