Maths-
General
Easy
Question
Let the unit vectors and be perpendicular and the unit vector be inclined at an angle θ to both and If then
- None of these
Hint:
We are given three unit vectors. Two of the vectors are perpendicular and the two vectors make same angle with the third be vector. We are given the third vector. We have to find the values of the variables of the third vector.
The correct answer is:
The given unit vectors are
So,
We are given that
The vectors makes angle θ with the vector .
The vector is given as
We have to find the values of .
Let's take the dot product of the vectors.
...( Both are perpendicular)
Let's substitute value of
We will substitute the value of
Now, we will do following multiplication
We have all the three values now.
We should know how to take dot product of two vectors.
Related Questions to study
Maths-
A random variable X has the probability distribution
For the events is prime number} and , the probability of is
A random variable X has the probability distribution
For the events is prime number} and , the probability of is
Maths-General
Physics-
Three long, straight and parallel wires carrying currents are arranged as shown in the figure. The wire C which carries a current of 5.0 amp is so placed that it experiences no force. The distance of wire C from wire D is then
Three long, straight and parallel wires carrying currents are arranged as shown in the figure. The wire C which carries a current of 5.0 amp is so placed that it experiences no force. The distance of wire C from wire D is then
Physics-General
Physics-
A 100 turns coil shown in figure carries a current of 2 amp in a magnetic field . The torque acting on the coil is
A 100 turns coil shown in figure carries a current of 2 amp in a magnetic field . The torque acting on the coil is
Physics-General
Physics-
Three long, straight and parallel wires carrying currents are arranged as shown in figure. The force experienced by 10 cm length of wire Q is
Three long, straight and parallel wires carrying currents are arranged as shown in figure. The force experienced by 10 cm length of wire Q is
Physics-General
Physics-
Four wires each of length 2.0 metres are bent into four loops P, Q, R and S and then suspended into uniform magnetic field. Same current is passed in each loop. Which statement is correct
Four wires each of length 2.0 metres are bent into four loops P, Q, R and S and then suspended into uniform magnetic field. Same current is passed in each loop. Which statement is correct
Physics-General
Physics-
A rectangular loop carrying a current i is situated near a long straight wire such that the wire is parallel to the one of the sides of the loop and is in the plane of the loop. If a steady current I is established in wire as shown in figure, the loop will
A rectangular loop carrying a current i is situated near a long straight wire such that the wire is parallel to the one of the sides of the loop and is in the plane of the loop. If a steady current I is established in wire as shown in figure, the loop will
Physics-General
Physics-
A very long straight wire carries a current . At the instant when a charge at point has velocity , as shown, the force on the charge is
A very long straight wire carries a current . At the instant when a charge at point has velocity , as shown, the force on the charge is
Physics-General
Physics-
In the given figure, the electron enters into the magnetic field. It deflects in .. direction
In the given figure, the electron enters into the magnetic field. It deflects in .. direction
Physics-General
Physics-
An electron (mass = 9× 10–31kg. Charge = 1.6 × 10–19C) whose kinetic energy is 7.2 × 10–18 joule is moving in a circular orbit in a magnetic field of 9 × 10–5 weber/m2. The radius of the orbit is
An electron (mass = 9× 10–31kg. Charge = 1.6 × 10–19C) whose kinetic energy is 7.2 × 10–18 joule is moving in a circular orbit in a magnetic field of 9 × 10–5 weber/m2. The radius of the orbit is
Physics-General
Physics-
Two particles A and B of masses and respectively and having the same charge are moving in a plane. A uniform magnetic field exists perpendicular to this plane. The speeds of the particles are and respectively, and the trajectories are as shown in the figure. Then
Two particles A and B of masses and respectively and having the same charge are moving in a plane. A uniform magnetic field exists perpendicular to this plane. The speeds of the particles are and respectively, and the trajectories are as shown in the figure. Then
Physics-General
Physics-
In the figure, what is the magnetic field at the point O
In the figure, what is the magnetic field at the point O
Physics-General
Physics-
A coil having N turns carry a current I as shown in the figure. The magnetic field intensity at point P is
A coil having N turns carry a current I as shown in the figure. The magnetic field intensity at point P is
Physics-General
Physics-
A current of 10A is passing through a long wire which has semicircular loop of the radius 20cm as shown in the figure. Magnetic field produced at the centre of the loop is
A current of 10A is passing through a long wire which has semicircular loop of the radius 20cm as shown in the figure. Magnetic field produced at the centre of the loop is
Physics-General
Physics-
A part of a long wire carrying a current i is bent into a circle of radius r as shown in figure. The net magnetic field at the centre O of the circular loop is
A part of a long wire carrying a current i is bent into a circle of radius r as shown in figure. The net magnetic field at the centre O of the circular loop is
Physics-General
Physics-
Two long straight wires are set parallel to each other. Each carries a current i in the same direction and the separation between them is 2r. The intensity of the magnetic field midway between them is
Two long straight wires are set parallel to each other. Each carries a current i in the same direction and the separation between them is 2r. The intensity of the magnetic field midway between them is
Physics-General