(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

The question states: "find all scalars c, if any exist such that given statement is true."

It also suggests trying to do without pencil and paper.

a) vector [c^{2}, c^{3}, c^{4}] is parallel to [1,-2,4] with same direction.

b) vector [13, -15] is a linear combination of vectors [1,5] and [3,c]

c) vector [-1,c] is a linear combination of vectors [-3,5] and [6,-11]

3. The attempt at a solution

a) for it to be parallel, it has to be a scalar multiple of [1,-2,4] = x. and [c^{2}, c^{3}, c^{4}] = y. then you can say ax = y. but wouldn't that give different values for all 3 c's? Lets say for example a=2. then 2x = y. then it would be:

i) c^{2}= 2*1

ii) c^{3}= 2*-2

iii) c^{4}= 2*4

which results in a different value of c in each. can i conclude that there DNE a such c?

b) the scalar multiple could be any real number for both vectors so c could be any real number?

c) 1[-3,5] + 1/3[6,-11] = [-1,4/3] so c = 4/3. this was achieved by trial and error. firstly is this even right? second, if its right, is there a algebraic way of doing it. it would have 3 unknowns and 2 equations.

at a glance seems pretty simple, or i just forgot some of the things i learned last year. any guidance would be appreciated.

**Physics Forums | Science Articles, Homework Help, Discussion**

Dismiss Notice

Join Physics Forums Today!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

# Homework Help: Vectors: Linear Combinations and Parallelism

**Physics Forums | Science Articles, Homework Help, Discussion**