Answer to Question #307577 in Analytic Geometry for Cynthia

Question

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.

⟩

Answer 1

Given

direction = < 3 , 4 , 3 >

length = 4

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

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

length = 4

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

9x² + 16² + 9x² =16

34x² = 16

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

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

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