Question

A= i+j+k and b=-i-j-k (a-b) will make an angle with a as

Answer 1

Answer:

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°

Answer 2

Answer:

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°