solve

Let the two vectors be A and B

A = A_x i + A_y j + A_z k

and B = B_x i + B_y j + B_z k

R₁ = i .... the position vector for point (1, 0, 0)

R₂ = k .... the position vector for point (0, 0, 1)

A.R₁ = AR₁cos45 = A_x

1/2 = A_x  .........Since A = 1, vector of unit length.

A = 1/2 i  or (1/2, 0 , 0)

Similarly,

B = 1/2 k or (0 , 0, 1/2)

Regards,

Team,

TopperLearning.