If diagonals of a parallelogram are then find the area of the parallelogram. - Wired Faculty

Question

If diagonals of a parallelogram are $straight P with rightwards arrow on top space and space straight Q with rightwards arrow on top comma$ then find the area of the parallelogram.

Solution

Let the sides of the parallelogram be $straight A with rightwards arrow on top space and space straight B with rightwards arrow on top$ , whose diagonals are $straight P with rightwards arrow on top space and space stack straight Q. with rightwards arrow on top$
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$equals space open vertical bar fraction numerator straight P with rightwards harpoon with barb upwards on top plus straight Q with rightwards harpoon with barb upwards on top over denominator 2 end fraction cross times fraction numerator straight P with rightwards harpoon with barb upwards on top minus straight Q with rightwards harpoon with barb upwards on top over denominator 2 end fraction close vertical bar space equals space 1 fourth open vertical bar open parentheses straight P with rightwards harpoon with barb upwards on top plus straight Q with rightwards harpoon with barb upwards on top close parentheses cross times open parentheses straight P with rightwards harpoon with barb upwards on top space minus space straight Q with rightwards harpoon with barb upwards on top close parentheses close vertical bar equals space 1 fourth open vertical bar open parentheses straight P with rightwards harpoon with barb upwards on top cross times straight P with rightwards harpoon with barb upwards on top space plus space straight Q with rightwards harpoon with barb upwards on top cross times straight P with rightwards harpoon with barb upwards on top space minus space straight P with rightwards harpoon with barb upwards on top space cross times straight Q with rightwards harpoon with barb upwards on top space minus space straight Q with rightwards harpoon with barb upwards on top space cross times space straight Q with rightwards harpoon with barb upwards on top close parentheses close vertical bar equals space 1 fourth open vertical bar open parentheses straight Q with rightwards harpoon with barb upwards on top cross times straight P with rightwards harpoon with barb upwards on top space plus straight Q with rightwards harpoon with barb upwards on top cross times straight P with rightwards harpoon with barb upwards on top close parentheses space space close vertical bar equals space 1 half space open vertical bar straight Q with rightwards harpoon with barb upwards on top cross times straight P with rightwards harpoon with barb upwards on top close vertical bar space equals space 1 half open vertical bar straight P with rightwards harpoon with barb upwards on top space cross times straight Q with rightwards harpoon with barb upwards on top close vertical bar$
Hence, the area of the parallelogram is found.

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Motion In A Plane

If diagonals of a parallelogram are $straight P with rightwards arrow on top space and space straight Q with rightwards arrow on top comma$ then find the area of the parallelogram.

Some More Questions From Motion in A Plane Chapter

Is a physical quantity, having a direction, necessarily a vector?

Name a quantity which is both scalar as well as vector.

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.

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For Daily Free Study Material Join wiredfaculty

Motion In A Plane

If diagonals of a parallelogram are then find the area of the parallelogram.

Some More Questions From Motion in A Plane Chapter

Is a physical quantity, having a direction, necessarily a vector?

Name a quantity which is both scalar as well as vector.

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.

Mock Test Series

NCERT Sample Papers

Entrance Exams Preparation

If diagonals of a parallelogram are $straight P with rightwards arrow on top space and space straight Q with rightwards arrow on top comma$ then find the area of the parallelogram.

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.