Question #307577

The vector that has the same direction as ⟨3,4,3⟩ but has length of 4 is ⟨ Blank 1. Calculate the answer by read surrounding text.


, Blank 2. Calculate the answer by read surrounding text.


, Blank 3. Calculate the answer by read surrounding text.



1
Expert's answer
2022-03-11T13:16:31-0500

Given

direction = < 3 , 4 , 3 >

length = 4

let the vector with direction be x < 3 , 4 , 3 > =

=< 3x , 4x , 3x >,

length = 4

(3x)2+(4x)2+(3x)2=4\sqrt{(3x)^2 + (4x)^2 + (3x)^2 } =4

9x2 + 162 + 9x2 =16

34x2 = 16

x=22/17x = 2\sqrt{2}/\sqrt{17}

x=22/17x = 2\sqrt{2/17}

vector=<62/17,82/17,62/17>vector = <6 \sqrt{2/ 17 }, 8\sqrt{2 /17} , 6\sqrt{2 /17}>


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