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 July 15th, 2019, 08:28 AM #1 Newbie   Joined: Jul 2019 From: India Posts: 11 Thanks: 0 Vector If the vector A = 2iˆ+4jˆ and B = 5iˆ+pjˆ are parallel to each other, the magnitude of B is____________ how to solve it?
July 15th, 2019, 08:39 AM   #2
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 Originally Posted by Indranil If the vector A = 2iˆ+4jˆ and B = 5iˆ+pjˆ are parallel to each other, the magnitude of B is____________ how to solve it?
if vector A and B are parallel, then vector B is a constant multiple of vector A ...

$\displaystyle 5\hat{i}+p\hat{j} = k(2\hat{i}+4\hat{j}) \implies 2k = 5 \text{ and } 4k=p$

solve for $p$, then $|\vec{B}| = \sqrt{5^2 + p^2}$

July 15th, 2019, 09:13 AM   #3
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 Originally Posted by skeeter if vector A and B are parallel, then vector B is a constant multiple of vector A ... $\displaystyle 5\hat{i}+p\hat{j} = k(2\hat{i}+4\hat{j}) \implies 2k = 5 \text{ and } 4k=p$ solve for $p$, then $|\vec{B}| = \sqrt{5^2 + p^2}$
I don't understand this concept 'then vector B is a constant multiple of vector A ...'
could you make this point easier for me with an easy example, please?

 July 15th, 2019, 09:33 AM #4 Math Team     Joined: Jul 2011 From: Texas Posts: 3,002 Thanks: 1587 two vectors ... $\vec{C} = 3\hat{i} + 4\hat{j}$ $\vec{D} = 6\hat{i} + 8\hat{j}$ note $\vec{D} = 2 \vec{C}$ both vectors have slope $\dfrac{4}{3}$, meaning they point in the same direction.

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