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

The vector (hat i +hat j) is a unit vector.

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) ?

Let a unit vector hat u = x hat i y hat j z hat k make angles (pi)2, (pi)/3 and (2 pi)/3 with the vectors frac{1}{sqrt 2} hat i frac{1}{sqrt 2} hat k , frac{1}{sqrt 2} hat j frac{1}{sqrt 2} hat k and frac{1}{sqrt 2} hat i frac{1}{sqrt 2} hat j respectively. If vec v = frac{1}{sqrt 2} hat i frac{1}{sqrt 2} hat j frac{1}{sqrt 2} hat k , then |hat u - vec v|^2

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) ?

The scalar product of the vector hat i+ hat j+ hat k with a unit vector along the sum of vector 2 hat i+4 hat j-5 hat k and lambda hat i+2 hat j+3 hat k is equal to one. Find the value of lambda .

The magnitude of the vector product of the vector hat i+hat j+hat k with a unit vector along the sum of vectors 2hat i+4hat j-5hat k and lambda i+2hat j+3hat k is equal to sqrt(2). Find the value of lambda_(.)

Find the angles which the vector vec a=hat i-hat j+sqrt(2)hat k makes with the coordinate axes.

Find the angles which the vector vec a=hat i-hat j+sqrt(2)hat k makes with the coordinate axes.

The unit vector along vec(A)= 2 hat i + 3 hat j is :

Show that vec a=(hati-hat j)/(sqrt(2)) is a unit vector.