Answer to Question #132108 in Calculus for Promise Omiponle

Question

1. Find the volume of the parallelpiped spanned by the vectors~A= i+j-k;~B=i-j+k;~C=-i+j+k

2. Assume that~A=<ax, 0, 0>;~B=<bx, by, bz>; and ~C=<cx, cy,cz>, and demonstrate that the following vector identity holds: Ax(BxC) = (A.C)B-(A.B)C

Note that if you replace the subscript "x" by "I","y" by"j", and "z" by "k", and then cycle x->y->z->x appropriately, you've proven the identity is true in general.

3. What is the cosine of the angle between the plane x+y+z= 5 and any of the coordinate planes? What about the cosine of the angle between x+y+z= 5 and x+ 2y+ 3z= 5?

4. What is the distance between the point (1, -2, 4) and the plane 3x+ 2y+ 6z= 5?

5. What is the distance between the parallel planes ax+by+cz=d1 and ax+by+cz=d2? You may wish to try picking a point on one plane that you can specify exactly and working out the distance from that point to the other plane.

Answer 1

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