Question

Please guys help me it's REALLY URGENT......

Answer 1

first of all

Let A=x i^ +y j^+z k^, B=a i^+b j^+ c k^.

from the eq.
Therefore, x+a=2.....(1) , x-a=4....(2). 
Adding (1)&(2), 
2x=6 
x=3. 
So, a = 2-x = 2-3 = -1. 


Similarly, y+b=6.....(3) , y-b=2.....(4) 
Adding (3)&(4), 
2y=8 
y=4. 
So, b = 6-y = 6-4 = 2. 

Finally, z+c=1....(5) , z-c= -11.....(6) 
Adding (5)&(6), 
2z=-10 
z=-5 
So, c = 1-z = 1-(-5) = 6. 


now we get
A = 3 i^ + 4 j^ - 5 k^, B = -1 i^ + 2 j^ + 6 k^. 

|A| = sq rt(x^2+y^2+z^2) = sq rt(9+16+25) = sq rt(50).
|B| = sq rt(1+4+36) = sq rt(41) . 

A.B is also represented by [(x*a)+(y*b)+(z*c)]. So, A.B here is equal to (3*[-1])+(4*2)+([-5]*6) = -3+8-30 = -25.
Hope you get it
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