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Motion in A Plane

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Physics Part I

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Physics

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Class 10 Class 12
Two vectors acting in opposite direction have resultant 7 units and if they act at angle 90° to each other, the resultant is 13 units. Calculate the magnitude of the two vectors.

Let A and B be the magnitude of two vectors straight A with rightwards arrow on top space and space straight B with rightwards arrow on top and let A>B.

When straight A with rightwards arrow on top space and space straight B with rightwards arrow on top act in opposite direction, the magnitude of resultant is A - B

Now,

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

When straight A with rightwards arrow on top space and space straight B with rightwards arrow on top act perpendicular to each other, then their resultant is,

                         square root of straight A squared plus straight B squared end root space equals space 13

rightwards double arrow              straight A squared plus straight B squared equals 169                   ...(2)

Now,             left parenthesis straight A squared plus straight B squared right parenthesis minus left parenthesis straight A minus straight B right parenthesis squared equals 2 thin space straight A thin space straight B

∴                    2 AB space equals space 169 minus left parenthesis 7 right parenthesis squared equals 120

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                             equals 169 plus 120 equals 289

or                 space space straight A plus straight B space equals space 17                    ...(3)

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

                A = 12 and B = 5


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What are the basic characteristics that a quantity must possess so that it may be a vector quantity?

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