If A=(2i-2j-k) and B= (i+j) ,then
(a) Find angle between A and B. (b) Find the projection of resultant vector of A and B on x-axis.
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Answer:
76.36° and 3
Explanation:
a) a=2i-2j-k
b=i+j
|a| =sqrt(2×2+2×2+1×1)=3
|b|=sqrt(1×1+1×1)=sqrt2=1.414
Cos(theta)= a.b/|a||b|
=(2i-2j-k)(i+j)/3×1.414
=(2-1-0)/4.242
=1/4.242
=0.2357
theta = acos(0.2357)
=76.36°
b)Resultant R =a+b= 2i-2j-k +i+j
R = 3i-j-k
Projection of Ŕ on x-axis
=Rcos(@)i
=(R.i)i/1
=((3i-j-k).i)i
=3
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