Motion in A Plane

Physics Part I

Physics

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Two vectors acting in opposite direction have resultant 7 units and if they act at angle 90Â° to each other, the resultant is 13 units. Calculate the magnitude of the two vectors.

Let A and B be the magnitude of two vectorsÂ Â and let A>B.

WhenÂ Â act in opposite direction, the magnitude of resultant is A - B

Now,

Â Â Â Â Â Â Â Â A - B Â = 7 [Given] Â Â Â Â Â Â Â ...(1)

WhenÂ Â act perpendicular to each other, then their resultant is,

Â Â Â Â Â Â Â Â Â Â Â Â Â

Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â ...(2)

Now, Â Â Â Â Â Â Â

âˆ´ Â Â Â Â Â Â Â Â Â Â

and Â Â Â Â Â Â

Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â

or Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â ...(3)

On solving equation (1) and (3), we get

Â Â Â Â Â Â Â Â A = 12 and B = 5

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What is a scalar quantity?

A physical quantity that requires only magnitude for its complete specification is called a scalar quantity.

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What is a vector quantity?

A physical quantity that requires direction along with magnitude, for its complete specification is called a vector quantity.

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