Calculus 3

[dusty garden]

1. Find the angles and the sides of the triangle determined by the points: P_1(1,2,3), P_2(3,1,-2), P_3(2,-3,-1).

2. Find the intersecting point of the plane through the points P_1(1,-1,1), P_2(3,-2,-1), P_3(1,0,-2) and the line through the points: P_4(1,2,1), P_5(3,-2,2).

3. Find the volume of the tetrahedron determined by the points: P_1(1,2,1), P_2(3,-2,2), P_3(2,3,-1), P_4(2,1,-1).

4. Find the parametric equation of the line that is the intersection of the two planes x+2y-3z = 4 and z=2x-3y-1.

5. Find the standard form of the equation of the plane determined by the parametric equation: x(s,t)=3-2s+t, y(s,t)=2+s-2t, z(s,t)=1+2s+2t.

6. For the three vectors →a = <1, 1, 1>, →b = <-1, 0, 1>, →c = <2, -1, -2> find two vectors →x and →y, such that →c = →x + →y, →x is in the plane determined by →a and →b, and →y is perpendicular to this plane.

Anyone can help me do these problems I don't understand the topics at all, can someone show the work to every problem, to every problem.

[somber mica]

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[rocky shadow]

"I don't understand the topics at all" then why are you solving these problems in the first place?

"can someone show the work to every problem" nope, you have much better chances if you show your work

1. calculate the vectors P1P2, P2P3 and P3P1, then find their lengths. The angles follow from the definition of dot product