The expression `(1/(sqrt(2))hat(i)+1/(sqrt(2))hat(j))` is a

What is the interior acute angle of the parallelogram whose sides are represented by the vectors (1)/(sqrt(2))hat(i)+(1)/(sqrt(2))hat(j)+hat(k) and (1)/(sqrt(2))hat(i) - (1)/(sqrt(2))hat(j)+hat(k) ?

What is the interior acute angle of the parallelogram whose sides are represented by the vectors (1)/(sqrt2) hat(i) +(2)/(sqrt2) hat(j) + hat(k) and (1)/(sqrt2) hat(i) - (1)/(sqrt2) hat(j) + hat(k) ?

The vector (1/sqrt2 hat i + 1/sqrt2 hat j) is a unit vector?

A particle is moving in xy -plane in circular path with centre at origin.If at an instant the position of particle is given by (1)/(sqrt(2))(hat i+hat j) .Then velocity of particle is along (A) (1)/(sqrt(2))(hat i-hat j) (B) (1)/(sqrt(2))(hat j-hat i) (C) (1)/(sqrt(2))(hat i+hat j) (D) Either (A) or (B)

Compute the magnitude of the following vectors : a = hat(i)+hat(j)+hat(k),b=2hat(i)-7hat(j)-3hat(k),c=(1)/(sqrt(3))hat(i)+(1)/(sqrt(3))hat(j)-(1)/(sqrt(3))hat(k) .

Let vec a=2hat i+hat j+hat k,hat b=hat i+2hat j-hat k and a unit vector vec c be coplanar.If vec c is perpendicular to vec a then vec c=+-(1)/(sqrt(2))(-hat j+hat k)( b) (1)/(sqrt(3))(-hat i-hat j-hat k)(1)/(sqrt(5))(hat o-2hat j)(d)(1)/(sqrt(3))(hat i-hat j-hat k)

A non-zero vector vec a is such that its projections along vectors (hat i+hat j)/(sqrt(2)),(-hat i+hat j)/(sqrt(2)) and hat k are equal,then unit vector along vec a is (sqrt(2)hat j-hat k)/(sqrt(3))b(hat j-sqrt(2)hat k)/(sqrt(3)) c.(sqrt(2))/(sqrt(3))hat j+(hat k)/(sqrt(3))d.(hat j-hat k)/(sqrt(2))