1.

If ` ve A = 3 hat I + 4 hat j` and ` vec B = 7 hat I + 24 hat j`. Find vector haveng the same magnitude as ` vec B` and parallel to ` vec A` .

Answer» The magnitude of `vec A` is,
` A = sqrt( 3^2 + 4^2 ) = 5` :
A unit vector parallel to `vec A` will be
` =hat A= hatA//A = ( 3 hat I + 4 hat j) //5` ltbRgt Now magnitude of ` vec B` is.
` B= sqrt ( 7^2 + ( 24) ^2) = 25` .
Therefore a vector parallel to ` vec A` and haveing magnitude of ` vec B` will be
` = 25 hat A = 25 ( 3hat i + 4 hat j) //5 = ( 15 hat i + 20 hat j)`.


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