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July 15th, 2019, 08:28 AM   #1
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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?
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July 15th, 2019, 08:39 AM   #2
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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 $|\vec{B}| = \sqrt{5^2 + p^2}$
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July 15th, 2019, 09:13 AM   #3
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Quote:
Originally Posted by skeeter View Post
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?
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July 15th, 2019, 09:33 AM   #4
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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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