Three vectors not lying in a plane can never end up to give a null vector. Is it true?

What is the value of \(\hat { i } +m\hat { j } ++\hat { k } \) to be unit vector?

Two equal forces having their resultant equal to either. At what angle are they inclined?

Under what condition the three vectors cannot give zero resultant?

What is the angle between A and B, if A and B denote the adjacent sides of a parallelogram drawn from a point and the area of the parallelogram is 1/2 AB?

A stone tied at the end of string is whirled in a circle. If the string breaks, the stone flies away tangentially. Why?

To a person moving eastwards with a velocity of 48km/h, rain appears to fall vertically downwards with a speed of 6.4km/h. Find the actual speed and direction of the rain.

A boat is moving with a velocity \(\left( 3\overset { \wedge }{ i } +4\overset { \wedge }{ j } \right) \)with respect to ground. The water in the river is moving with a velocity\(-3\overset { \wedge }{ i } -4\overset { \wedge }{ j } \)with respect to water?

A stone is thrown vertically upwards and then it returns to the thrower. Is it a projectile?

When do we say two vectors are orthogonal?

Explain the property of two vectors A and B if \(|\mathbf{A}+\mathbf{B}|=|\mathbf{A}-\mathbf{B}|\)

A passenger arriving in a new town wishes to go from the station to a hotel located 10 km away on a straight road from the station. A dishonest cabman takes him along a circuitous path 23 km long and reaches the hotel in 28 min. What is
(a) the average speed of the taxi,
(b) the magnitude of average velocity ? Are the two equal ?

A bullet fired at an angle of 30^o with the horizontal hits the ground 3 km away. By adjusting its angle of projection, can one hope to hit a target 5 km away? Assume the muzzle speed to be fixed, and neglect air resistance?

A cricket can throw a ball to a maximum horizontal distance of 100 m. With the same speed, how high above the ground can the cricketer throw the same ball?
Horizontal range is maximum when angle of projection is 45^o .

An aircraft is flying at a height of 3400 m above the ground. If the angle subtended at a ground observation point by the aircraft positions 10.0 s a part is 30°, wat is the speed of the aircraft ?

Determine a unit vector which is perpendicular to both  \(A=2\hat { i } +\hat { j } +\hat { k } \)  and \(B=\hat { i } -\hat { j } +\hat { k } \)          

The ceiling of a long hall is 25 m high. What is the maximum horizontal distance that a ball thrown with a speed of 40 m s-1 can go without hitting the ceiling of the hall ?

The range of a rifle bullet is 1000m, when \(\theta \) is the angle of projection. If the bullet is fired with the same angle from a car travelling at 36km/h towards the target, show that the range will be increasing by 142.9\(\sqrt { tan\theta m } \).
When the bullet is fired from the moving car, the horizontal component velocity of the bullet increases with the velocity of car. But the vertical component of the velocity remains uneffected.

Rain is falling vertically with a speed of 30 m/s. A woman rides a bicycle with a speed of 10 m/s in the North to South direction. What is the direction in which she should hold her umbrella?

In a harbour, wind is blowing at the speed of 72 km/h and the flag on the mast of a boat anchored in the harbour flutters along the N-E direction. If the boat starts moving at a speed of 51 km/h to the North, what is the direction of flag on the mast of the boat?

A cyclist is riding with a speed of 27kmh^-1. As he approaches, a circular turn on the road of f radius 80 m, he applies brakes and reduces his speed at the constant rate of 0.5 ms^-2.What is the magnitude and direction of the net acceleration of the cyclist on the circular turn?

A ball rolls of the top of a stairway with horizontal velocity of 1.8 m/s. The steps are 0.24 m high and 0.2 m wide. Which step will the ball hit first? Take g=9.8 m/s²

A machine gun is mounted on the top of a tower 100m high. At what angle should the gun be inclined to cover a maximum range of firing on the ground below? The muzzle speed of the bullet is 150 m/s. Take g=10 m/s²