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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
For the three vectors shown in the figure, the vector sum \vec {D} = \vec {A} + \vec {B} + \vec {C} has components D_x = 3 and D_y = 0.(
Find a . b and a X b if a=i+2j+k and |b| = 3 acting along c = i + j + k.
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.
If A, B, C are any three vectors then show that AX(B+C) = AXB+AXC.
The resultant of scalar product and vector product of two given vectors is zero. If one vector is i. What is the other vector??
find the point of intersection of planes in vector form ('.' refers to dot product) r.a=1,r.b=1 ,r.c=1 where a,b,c are non co-planner vectors.
Evaluate the surface integral double integral s F * dS for the given vector field F and the oriented surface S. In other words, find the flux of F across S. For closed surfaces, use the positive (outward) orientation.

F(x,y,z) = xyi + 12x^2j + yzk
S is the surface z = xe^y, 0 less than or equal to x less than or equal to 1, 0 less than or equal to y less than or equal to 4, with upward orientation.
What do you understand by divergence of a vector field? What is the meaning of positive, negative, and zero divergence?
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