1. If a is a real constant, determine the volume V of the parallelepiped spanned by...

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1. If a is a real constant, determine the volume V of the parallelepiped spanned by the vectors (a, -3,0), (5, a, 2), (1,5, a). Show that there is exactly one real value of a for which V vanishes, and give a geometric explanation of why the volume is zero in this case. 2. Two points U and V in R' are defined by their position vectors u = (1,2,3, 4, 5,6, 7) and v = (0,1,0, 1,0, 1,0) respectively. If w is the vector pointing from V to U, find the length of w, and the angle between w and u. 1. If a is a real constant, determine the volume V of the parallelepiped spanned by the vectors (a, -3,0), (5, a, 2), (1,5, a). Show that there is exactly one real value of a for which V vanishes, and give a geometric explanation of why the volume is zero in this case. 2. Two points U and V in R' are defined by their position vectors u = (1,2,3, 4, 5,6, 7) and v = (0,1,0, 1,0, 1,0) respectively. If w is the vector pointing from V to U, find the length of w, and the angle between w and u.