Finding coefficients so aA+bB+C is parallel to y-axis

[formulajoe]

ive been struggling with these for an hour and a half.
they arent hard, i just can't seem to make them work.
the first one is:
A = (5,3,2)
B = (-1,4,6)
C = (8,2,0)

im using this format (x,y,z)

aA+bB+ C = a vector parallel to the y-axis.
so, that means i need to find a vector with only z components right?
well, the answers out of the back of the book are a = -12/7 and b = -4/7.
these don't work out.



heres the second one
A = (a,1,4)
B = (3,b,-6)
C = (5,-2,c)

Im supposed to find a,b, and c so that all three vectors are perpendicular to each other.
that means i should use the dot product with A and B, A and C, and B and C and set the dot product equal to zero for all three. So I did this, and i got answers for a, b and c but they don't work out when i check them.

 

[vincentchan]

if a vector is parallel to y axis, that's means the vector is pointing at y direction... so what will the x and z component of this vector be? after you have the x and z component.. what you ganna to is write down the equation for x&z component... then you will have 2 equation, with 2 unkn..for the 2nd problem, your method is completely fine... check your algebra again

 

[formulajoe]

okay, i tried this
5a -b + 8 = 1
3a + 4b +2 = 0
this leaves a 1 in x, and a 0 in y

i solved it this way, and got close to the right answer. am i on the right track?

 

[formulajoe]

okay, this way should be right
5a - b = -8
2a + 6b = 0
a = -1.5
b = .5
maybe the answers in the back of the book are wrong?

 

[Leo32]

Hi Formulajoe,

Did you consider the questions of Vincenchan ?
If a vector should be parallel to the y axis, what requirements can you put on the x, y, z coördinates. I'm sure you can work out the algebra to calculate the solutions, but I've got the impression you're a bit in the vague as to what you need to calculate...

Greetz,
Leo

 

[clive]

Hi formulajoe,

you're right. Your solution is correct. Maybe the answers in your book are wrong.

 

[Galileo]

If a = -12/7 and b = -4/7 then the z-component of aA+bB+C is:
(-12/7)(2)-(4/7)(6)+0=-48/7

So it is not parallel to the y-axis.
Check if you read the question correctly. If you did, then the books answer if wrong.