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

Solution

Let PQR be triangle formed by vectors $straight A with rightwards arrow on top space and space straight B with rightwards arrow on top$ shown in figure.

From figure, the area of $increment PQR$ is,
$straight S equals 1 half PQ. RN space space equals 1 half PQ. PR space sinθ$
$space space equals 1 half ABsinθ space equals space 1 half open vertical bar straight A with rightwards arrow on top cross times straight B with rightwards arrow on top close vertical bar$

Some More Questions From Motion in A Plane Chapter

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 a triangle represent the two vectors, then area of the triangle is equal to half of the magnitude of the cross product of two vectors.

Some More Questions From Motion in A Plane Chapter

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.

What is module of vector?

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 a triangle represent the two vectors, then area of the triangle is equal to half of the magnitude of the cross product of two vectors.

Some More Questions From Motion in A Plane Chapter

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.

What is module of vector?

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.