SOLUTION: What's the component form of the vector {{{ V }}} with ||v|| = {{{ 12 }}}, in the same direction as {{{ U }}} = <3, -5>? Thanks.

Algebra ->  Test -> SOLUTION: What's the component form of the vector {{{ V }}} with ||v|| = {{{ 12 }}}, in the same direction as {{{ U }}} = <3, -5>? Thanks.      Log On


   



Question 1075694: What's the component form of the vector +V+ with ||v|| = +12+, in the same direction as +U+ = <3, -5>? Thanks.
Answer by Fombitz(32388) About Me  (Show Source):
You can put this solution on YOUR website!
Find the unit vector for U.
abs%28U%29=sqrt%283%5E2%2B%28-5%29%5E2%29
abs%28U%29=sqrt%289%2B25%29
abs%28U%29=sqrt%2834%29
So then,
U%5BU%5D=(3%2Fsqrt%2834%29,-5%2Fsqrt%2834%29)
Multiply the U unit vector by the magnitude of V to get vector V,
V=12*(3%2Fsqrt%2834%29,-5%2Fsqrt%2834%29)
V=(36%2Fsqrt%2834%29,-60%2Fsqrt%2834%29)
V=(%2836%2F34%29sqrt%2834%29,-%2860%2F34%29sqrt%2834%29)
V=(%2818%2F17%29sqrt%2834%29,-%2830%2F17%29sqrt%2834%29)