If \(\overrightarrow { { a }_{ 1 } } \) and \(\overrightarrow { { a }_{ 2 } } \) are two non collinear unit vectors and if \(\left| \overrightarrow { { a }_{ 1 } } +\overrightarrow { { a }_{ 2 } } \right| \) =\(\sqrt{3}\), then the value of \(\left( \overrightarrow { { a }_{ 1 } } -\overrightarrow { { a }_{ 2 } } \right) .\left( 2\overrightarrow { { a }_{ 1 } } +\overrightarrow { { a }_{ 2 } } \right) \) is

The sum of magnitudes of two forces acting at a point is 18 units and the magnitude of their resultant is 12 units. The resultant is at 90° with the force of the smaller magnitude. The magnitude of the individual forces is

If the resultant of three forces \(\overrightarrow { F } _{ 1 }=p\hat { i } +3\hat { j } -\hat { k } ,\overrightarrow { F } _{ 2 }\)and \(\overrightarrow { F } _{ 3 }=6\hat { i } -\hat { k } \) acting on a particle has a magnitude equal to 5 units, then the value of p is

A particle moves on a given line with a constant speed \(\upsilon \). At a certain time it is at a point P on its straight line path. O is fixed point. The value of \(\overrightarrow { OP } \times \overrightarrow { \upsilon } \) is (where y is perpendicular distance from O to given line)

From the top of a tower of height 40 m, a ball is projected upwards with a speed of 20 m/ s at an angle of elevation of 30°. The ratio of the total time taken by the ball to hit the ground to its time of flight (time taken to come back to the same elevation) is (Take g = 10 m/s²)

At the top of the trajectory of a projectile, the directions of its velocity and accelerations are

A plane is indined at an angle of 30° with horizontal. The magnitude of component of a vector \(\overset\rightarrow{A}\)=-10\(\hat{k} \) perpendicular to this plane is (here z-direction is vertically upwards

The dot product of two vectors vanished when vectors are orthogonal and has maximum value when vectors are parallel to each other.Explain

The angle between vector A and B is 60⁰  .What is the ratio of A.B and \(\left| A\times B \right| \) ?

What conclusion do you draw about  \(​​​​\overset\rightarrow{B}\), if \(​​​​\overset\rightarrow{A}\)-\(​​​​\overset\rightarrow{B}\)=\(​​​​\overset\rightarrow{A}\)+\(​​​​\overset\rightarrow{B}\) ?

What is the angle between velocity vector and acceleration vector in uniform circular motion?

A body is projected in horizontal direction with a uniform velocity from top of tower. Show that the path is parabola.

Define centripetal acceleration. Give two examples.

A body is projected with the velocity u₁ from the point A as shown in figure. At the same time another body is projected vertically upwards with the velocity U₂ from the point B. What should be the value of u₁/u₂ for both the bodies to collide?

A particle starts from origin at t = 0 with a velocity 15\(\overset { \wedge }{ i } \)m/s and moves in xy-plane under the action of a force which produces a constant acceleration of 15\(\overset { \wedge }{ i } \)+10\(\overset { \wedge }{ j } \)\({ m }/{ s^{ 2 } }\).Find the y-coordinate of the particle at the instant.Its x-coordinate is 125m.

A man moves towards East with velocity 6\({ ms }^{ -1 }\)and another man B moves in N \(-30^{ \circ }E\)with 6\({ ms }^{ -1 }\)> Find the velocity of B w.r.t A.

State the reason , whether the following algebraic operations with scalar and vector physical quantities are meaningful
Multiplying any two scalars

State the reason , whether the following algebraic operations with scalar and vector physical quantities are meaningful
Adding any two vectors