A unit vector a makes an angle `pi/ 4` with z-axis. If `a + i + j` is a unit vector, then a can be equal to

Define unit vector .

If a unit vector vec a makes angles pi/3 with hat i ,pi/4 with hat j and an acute angle theta with hat k , then find the value of theta .

A unit vector is used to specify

If a unit vector vec a makes angles (pi)/(3) with hat i , (pi)/(4) with hat j and an acute angle theta with hat k , then find theta and hence, the components of vec a .

Vector 1/3(2i-2j+k) is (A) a unit vector (B) makes an angle pi//3 with vector (2 hat i-4 hat j+3 hat k) (C) parallel to vector (- hat i+ hat j-1/2 hat k) (D) perpendicular to vector 3 hat i+2 hat j-2 hat k

If vec a , vec b ,a n d vec c are there mutually perpendicular unit vectors and vec d is a unit vector which makes equal angles with vec a , vec b ,a n d vec c , the find the value off | vec a+ vec b+ vec c+ vec d|^2dot

A vector vecA makes an angle of 20^@ and vecB makes an angle of 110^@ with the X-axis. The magnitude of these vectors are 3 m and 4 m respectively.Find the resultant