Question

if vectors are A= i+j+k and vector B = -i-j-k,then find the angle between vector (A - B) and A.

Answer 1

V(A-B)= (1+1)i +(1+1)j+ (1+1)k
          = 2i+2j+2k
V(A)=i+j+k

Angle between two vectors is given as
cosФ= V(A-B).V(A) / IV(A-B)I IV(A)I
where V(A-B).V(A) means scalar product or the dot product and 
 IV(A-B)I IV(A)I means product of modulus of vector V(A-B) and V(A) respectively.

Hence from this we get 

cosФ= 2*1+2*1+2*1 / (√2²+2²+2²)(√1²+1²+1²)
cosФ= 6/(2√3)(√3)
cosФ= 6/6
cosФ=1 
hence 
cosФ=1 at 0°,180°
hence 
Ф=0° Ans
           

Answer 2

this is the answer
the answer may be 180 and 0 degree