Vector Calculus Answers

Find the equation of the plane through (1,2,-2) that contains the line x=2t, y=3-t z=1+3t

Find a vector (in 2 space) of length 2 that is parallel to the curve y=x^(2/3) at the point (-8,4)

If A=2i+j+k, B=i-2j+2k, and C=3i-4j+2k, find the projection of A+C in the direction of B.

A triangle has vertices at A(2,3,1), B(-1,1,2), C(1,-2,3). Find a) The length of the median drawn from B to side AC and b)The acute angle which this median makes with side BC.

If A=2i+j+k, B=i-2j+2k, and C=3i-4j+2k, find the projection of A+C in the direction of B.

Find a unit vector in the direction of the resultant of vectors A=2i-j+k, B=i+j+2k, C=3i-2j+4k.

Suppose the sides of a closed polygam represent vector arrangend head to tail rule , what is sum of these vectors ?

Show that the sum and difference of two perpendicular vectors of equal lengths are also perpendicular and of some lengths ?

Two workers are pulling on ropes attached to a tree stump one of them pull by 50 N and another one pull by 40 N the angle between tow forces is 60 degree . Find the magnitude and direction of the resultant force on the tree.

Given three points A=(2, -3, 4), B=(0, 1, 2), and C=(-1, 2, 0) in a 3-D coordinate systems. Find the area of the triangle with A, B, and C as vertices.