A particle moves along straight line such that at time t its position from a fixed point O on the line is . The velocity of the particle when t=2 is:
(A)
(B)
(C)
(D)
Coordinates of a moving particle are given by and . The speed of the particle is given by
(1)
(2)
(3)
(4)
The x and y components of vector are 4m and 6m respectively. The x, y components of vector are 10m and 9m respectively. The length of is ______ and angle that makes with the x axis is given by _______.
(A)
(B)
(C)
(D)
A particle travels with speed 50 m/s from the point (3, 7) in a direction . Find its position vector after 3 seconds.
1.
2.
3.
4.
If \(\overrightarrow{a}\) is a vector and \(x\) is a non-zero scalar, then which of the following is correct?
1. | \(x\overrightarrow{a}\) is a vector in the direction of \(\overrightarrow{a}\). |
2. | \(x\overrightarrow{a}\) is a vector collinear to \(\overrightarrow{a}\). |
3. | \(x\overrightarrow{a}\) and \(\overrightarrow{a}\) have independent directions. |
4. | \(x\overrightarrow{a}\) is a vector perpendicular to \(\overrightarrow{a}\). |
If \(\theta\) is the angle between two vectors and , and , then \(\theta\) is equal to:
1. \(0^\circ\)
2. \(180^\circ\)
3. \(135^\circ\)
4. \(45^\circ\)
The vector \(\overrightarrow b\) which is collinear with the vector \(\overrightarrow a = \left(2, 1, -1\right)\) and satisfies the condition \(\overrightarrow a. \overrightarrow b=3\) is:
1. \(\left(1, \frac{1}{2}, \frac{-1}{2}\right)\)
2. \(\left(\frac{2}{3}, \frac{1}{3}, \frac{-1}{3}\right)\)
3. \(\left(\frac{1}{2}, \frac{1}{4}, \frac{-1}{4}\right)\)
4. \(\left(1, 1, 0\right)\)
If a, b and c are three non-zero vectors such that , then the value of will be:
1. | Less than zero | 2. | equal to zero |
3. | greater than zero | 4. | 3 |
Two vectors and inclined at an angle with respect to each other have a resultant which makes an angle with . If the directions of and are interchanged, then the resultant will have the same
(A) magnitude
(B) direction
(C) magnitude as well as direction
(D) neither magnitude nor direction
Two vectors and lie in a plane. Another vector lies outside this plane. The resultant of these three vectors
(1) can be zero
(2) cannot be zero
(3) lies in the plane of
(4) lies in the plane of