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Scrat [10]
3 years ago
9

How do you find a vector of length 10 in the direction of v= <3,-2>?

Mathematics
2 answers:
jonny [76]3 years ago
6 0
Let x<span> be the vector we seek. We recall the relationship of a vector to its length and direction:
</span><span>dir x=<span>x/<span>|x|</span></span></span>Because we art trying to find x from information on its length and direction, we rewrite this formula as,<span>x=|x| dir x.</span>We are given that <span>|x|=13</span> We need to compute <span>dir x</span> from the information that x is in the same direction as <span>⟨1,−1⟩</span>:<span>dir x=dir ⟨3,−2⟩=<span><span>⟨3,−2⟩</span><span>|⟨3,−2⟩|</span></span>.</span>We need to compute the length <span>|⟨3,−2⟩|</span>. To do this, recall thatThe length of the vector <span>y=⟨<span>y1</span>,<span>y2</span>⟩</span> is <span>|y|=<span><span><span>y21</span>+<span>y22</span></span><span>−−−−−−</span>√</span></span>.Hence, <span>|⟨3,−2⟩|=√13</span>,<span>.</span>Thus 
<span>x=</span><span>√</span>13
Katena32 [7]3 years ago
5 0
Hello,

We are going to used the theorem of Thalès.

||v||=√(3²+(-2)²)=√13

k*√13=10==>k=10/√13

w=k.v=10/√13<3,-2>

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