math
posted by yuni .
the position vectors of the point A,B & C respect to O are a=3i2j+4k, b=i+3j4k, c=2i+5j3k. Find
a)the angle between a+b and ab
b)lamdar if vector a is perpendicular to b+lamdar k.

How do you define "lambdar" ?
As for part (a), compute these two vectors:
a + b = 4i +j +0k
a  b = 2i 5j +4k
Their magnitudes are:
a+b = sqrt(16 + 1) = sqrt17
ab = sqrt(4 +25 + 16) = sqrt45
(a+b)*(ab) = 8 5 = 3
= (sqrt17) x (sqrt45) cos theta
cos theta = 3/sqrt765 = 0.108
theta = 83.8 degrees
In the above, * denotes a dot product and x denotes normal scalar multiplication