Show that if two adjacent sides of parallelogram represent the two vectors, then area of the parallelogram is equal to magnitude of the cross product of two vectors.

Solution

As shwn in the fig., et PQRS be a parallelogram formed by vectors $straight A with rightwards arrow on top space and space straight B with rightwards arrow on top$ .

From the figure,
Area of parallelogram PQRS is given by,
S = PQ. RN
= $PQ. space PR space sinθ space equals space straight A space straight B space sinθ$
$space space equals open vertical bar straight A with rightwards arrow on top cross times straight B with rightwards arrow on top close vertical bar$
Hence the result.

Some More Questions From Motion in A Plane Chapter

Which of the followings is/are vector quantities: work, power, acceleration, mass, momentum?

Pick up the odd one from the following: force, linear momentum, mass, impulse.

Pick out the only vector quantities in the following list:
Temperature, pressure, impulse, time, power, total path length, energy, gravitational potential, coefficient of friction and charge.

Pick out the two scalar quantities in the following list:
force, angular momentum, work, current, linear momentum, electric field, average velocity, magnetic moment, reaction as per Newton’s third law, relative velocity.

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Motion In A Plane

Show that if two adjacent sides of parallelogram represent the two vectors, then area of the parallelogram is equal to magnitude of the cross product of two vectors.

Some More Questions From Motion in A Plane Chapter

Which of the followings is/are vector quantities: work, power, acceleration, mass, momentum?

Pick up the odd one from the following: force, linear momentum, mass, impulse.

Pick out the only vector quantities in the following list:
Temperature, pressure, impulse, time, power, total path length, energy, gravitational potential, coefficient of friction and charge.

Pick out the two scalar quantities in the following list:
force, angular momentum, work, current, linear momentum, electric field, average velocity, magnetic moment, reaction as per Newton’s third law, relative velocity.

What are polar vectors?

Give two examples of polar vectors.

What are axial vectors?

Give two examples of axial vectors.

What are tensors?

Give one example of tensor.

Mock Test Series

NCERT Sample Papers

Entrance Exams Preparation

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For Daily Free Study Material Join wiredfaculty

Motion In A Plane

Show that if two adjacent sides of parallelogram represent the two vectors, then area of the parallelogram is equal to magnitude of the cross product of two vectors.

Some More Questions From Motion in A Plane Chapter

Which of the followings is/are vector quantities: work, power, acceleration, mass, momentum?

Pick up the odd one from the following: force, linear momentum, mass, impulse.

Pick out the only vector quantities in the following list:Temperature, pressure, impulse, time, power, total path length, energy, gravitational potential, coefficient of friction and charge.

Pick out the two scalar quantities in the following list: force, angular momentum, work, current, linear momentum, electric field, average velocity, magnetic moment, reaction as per Newton’s third law, relative velocity.

What are polar vectors?

Give two examples of polar vectors.

What are axial vectors?

Give two examples of axial vectors.

What are tensors?

Give one example of tensor.

Mock Test Series

NCERT Sample Papers

Entrance Exams Preparation

Pick out the only vector quantities in the following list:
Temperature, pressure, impulse, time, power, total path length, energy, gravitational potential, coefficient of friction and charge.

Pick out the two scalar quantities in the following list:
force, angular momentum, work, current, linear momentum, electric field, average velocity, magnetic moment, reaction as per Newton’s third law, relative velocity.