Question

Find a vector which is parallel to v=i-2j


;
and has a magnitude 10.​

Answer 1

Answer:

$2 \sqrt{5} i - 4 \sqrt{5} j$

Explanation:

$v = i - 2j \\ \\ unit \: \: vector \: parallel \: to \: v \: is \: \frac{v}{ |v| } \\ \\ |v| = \sqrt{1 + 4} = \sqrt{5} \\ \\ now \: \: v {}^{?} = \frac{i - 2j}{ \sqrt{5} } \\ \\ now \: a \: vector \: of \: 10 \: units \: \: magnitude \: parallel \: to \: \: v \: \: is \\ \\ w = 10( \frac{i - 2j}{ \sqrt{5} } ) \\ \\ w = 2 \sqrt{5} i - 4 \sqrt{5} j$

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