Question

Vectors parallel to 6i+8j and having a magnitude of 5

Answer 1

Explanation:

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Answer 2

Answer:

The required vectors are $3\hat i+4\hat j,3\hat i-4\hat j,-3\hat i-4\hat j\:and\:-3\hat i+4\hat j$

Explanation:

Let the given vector be $\vec p=6\hat i+8\hat j$ and let $\vec q=a\hat i+b\hat j$ be the vector which has a magnitude of 5 units and is parallel to the given vector.

As magnitude is 5 units,we can write

$\sqrt{a^{2}+b^{2}} =5= > a^{2}+b^{2}=25-- > (1)$

If two vectors $a_{1}\hat i+b_{1}\hat j$ and $a_{2}\hat i+b_{2}\hat j$ are parallel to each other than,

$\frac{a_{1}}{a_{2}} =\frac{b_{1}}{b_{2}}$

Similarly for our given vector and required vector,we can write

$\frac{a}{6} =\frac{b}{8} = > a=\frac{3b}{4}-- > (2)$

Substituting equation 2 in equation 1,we get

$(\frac{3b}{4})^{2}+b^{2}=25= > \frac{25b^{2}}{16}=25= > b=\pm 4$

Substituting the value of b in equation 2,we get

$a=\frac{3(\pm 4)}{4}=\pm 3$

The values of a and b are $a=\pm 3,b=\pm 4$

Therefore,

The required vectors are $3\hat i+4\hat j,3\hat i-4\hat j,-3\hat i-4\hat j\:and\:-3\hat i+4\hat j$

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