- #1

CaliforniaRoll88

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- Homework Statement
- The vector from the origin to point ##A## is given as ##(6,-2,-4)##, and the unit vector directed from the origin toward point ##B## is ##(2,-2,1)/3##. If points ##A## and ##B## are ten units apart, find the coordinates of point ##B##.

- Relevant Equations
- ##\left |\vec r\right |=10##

##\hat a_B=\frac {\vec B}{\left |\vec B\right |}={\frac {\vec B}{\sqrt {B^2_x+B^2_y +B^2_z}}}##

##\left| \vec r\right |=\sqrt {(x_B-x_A)^2+(y_B-y_A)^2+(z_B-z_A)^2}##

Ans:##(7.8,-7.8,3.9)##

##\hat a_B=\frac 2 3\hat a_x-\frac 2 3\hat a_y+\frac 1 3\hat a_z##

##\left| \vec r\right |=\sqrt {(x_B-6)^2+(y_B+2)^2+(z_B+4)^2}=10##

##\left |\vec A\right |=\sqrt {6^2+2^2+4^2}=\sqrt {5}{6}##

Not sure where to go from here. Please help!

Source: Problem 1.3; Engineering Electromagnetics, 8th Edition, William Hayt, John Buck

##\left| \vec r\right |=\sqrt {(x_B-6)^2+(y_B+2)^2+(z_B+4)^2}=10##

##\left |\vec A\right |=\sqrt {6^2+2^2+4^2}=\sqrt {5}{6}##

Not sure where to go from here. Please help!

Source: Problem 1.3; Engineering Electromagnetics, 8th Edition, William Hayt, John Buck