Vector Calculus Answers

If u = i + 3j - 2k, and v = 4i - 2j - 4k. Find ( 2u + v ) ( u - 2v ).

find the unit vecter in the direction of a=i+j+k

Given that :
r−1=6i−8j+2k, r2=4i+5j+7k, r3=−2i+j+6k is a vector.Findr1r2

A body is in equilibrium under the action of three force vectors A, B and C simultaneously. Show that A X B = B X C = C X A.

The resultant of scalar product and vector product of two given vectors is zero. If one vector is i. What is the other vector??

What do you understand by divergence of a vector field? What is the meaning of positive, negative, and zero divergence?

A triangle has vertices A (-1, 3, 4) B (3, -1, 1) and C (5, 1, 1). The area of ABC is
a) 30.1
b) 82.1
c) 9.1
d) 52.1

Find the intersection of the planes x+ (y-1)+z=0 and -x + (y+1)- z+0

how do I find an equation for the plane that passes through the point ( 2,-1 3) and is perpendicular to to the line v= (1,-2,2,)=+t(3,-2,4)

PROVE that d/du(AxB) = Ax(dB/du) + (dA/du)xB where A,B are differentiated functions of u.