Question

If A=3i+4j and B=7i+24j then find the vector having the same magnitude as B and same direction as A.

Answer 1

$if \: \bold{A} \: = 3i + 4j \\ then \\ \hat{A} \: = \frac{3}{5}i + \frac{4}{5}j \\ since \: | |A| | = \sqrt{ {3}^{2} + {4}^{2} } = 5$
now,

$| |B| | = \sqrt{ {7}^{2} + {24}^{2} } = 25$
so, a vector C having magnitude B and Direction  is,
$\\ \bold{C} \: = 25( \frac{3}{5}i + \frac{4}{5}j ) \\ or \\ \bold{C} \: =15i + 20j$
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