The vector ` hat i+x hat j+3 hat k` is rotated through an angle `theta` and doubled in magnitude, then it becomes `4 hat i+(4x-2)dot hat j+2 hat k` . Then value of `x` are `-2/3` (b) `1/3` (c) `2/3` (d) 2

The vector hat(i)+xhat(j)+3hat(k) is rotated through an angle theta and doubled in magnitude then it becomes 4hat(i)+(4x-2)hat(j)+2hat(k) . The value of x is

The magnitude of the vector hat(i)+xhat(j)+3hat(k) is half of the magnitude of vector 4hat(i)+(4x-2)hat(j)+2hat(k) . The values of x are ?

Find the angle between the vectors hat i-2hat j+3hat k and 3hat i-2hat j+hat k

The magnitude of the component of the vector (2 hat i+3 hat j + hat k) along (3 hat I = 4 hat k) is .

Determine the sine of the angle between the vectors . 2 hat I + 3 hat j -4 hat k and ( hat i-2 hat k).

The vectors 3 hat i- hat j +2 hat k', 2 hat i+hat j + 3 hat k and hat i + lambda hat j - hat k are coplaner if value of lambda is (A) -2 (B) 0 (C) 2 (D) any real number

The vectors hat(i)- 2x hat(j) - 3y hat(k) and hat(i) + 3x hat(j) + 2y hat(k) are orthogonal to each other. Then, the locus of the point (x, y) is:

Let ABCD be the parallelogram whose sides AB and AD are represented by the vectors 2 hat i +4 hat j-5 hat k and hat i+2 hat j+3 hat k.Then if vec a is a unit vector parallel to AC then = (a) 1/3(3 hat i-6 hat j-2 hat k) (b) 1/3(3 hat i +6 hat j+2 hat k) (c) 1/7(3 hat i +6 hat j+2 hat k) (d) 1/7(3 hat i +6 hat j-2 hat k)

If 9 3hat i-2 hat j+ 2 hat k+ 2hat k).(2 hat i-x hat j+3 hat k) =- 12 , the value of (x) is .

Find the vector of magnitude 3, bisecting the angle between the vectors vec a=2hat i+hat j-hat k and vec b=hat i-2hat j+hat k