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Equal Vectors

If A=3i+4j an...

Question

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

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Solution

The vector must be parallel to A and having magnitude equal to B will be
magnitude of B x UNIT VECTOR OF A
$t h e m a g n i t u d e o f A = \sqrt{3^{2} + 4^{2}} = \sqrt{9 + 16} = \sqrt{25} = 5 h e n c e u n i t v e c t o r o f A = \frac{\underset{A}{\to}}{|A|} = \frac{3 i + 4 j}{5} n o w m a g n i t u d e o f B = \sqrt{7^{2} + 24^{2}} = \sqrt{625} = 25 h e n c e 25 \times u n i t v e c t o r o f A 25 \times \frac{3 i + 4 j}{5} = 5 (3 i + 4 j) .$

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Similar questions

\to a = 3^i + 4^j

\to b = 7^i + 24^j

, then find the vector having the same magnitude as

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and same direction as

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\to a = 3^i + 4^j

\to b = 7^i + 24^j

, then find the vector having the same magnitude as

\to b

and same direction as

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Q. If two vectors

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\to a = 3^i + 4^j

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then a vector having the same magnitude as

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