The force on an object is F⃗ =−15j⃗ . For the vector v⃗ =−i⃗ −3j⃗ , find:?
The component of F⃗ parallel to v⃗ .
I get my answer to be: 45/sqrt[10], but i guess it's wrong cuz it's saying that it is =p
Update:It tells me that the answer is a vector, not a real number. 45/sqrt[10] is a real number, i need a vector number. How do i get that?
More Questions From This User See All
Answers & Comments
No you are right.
projection of F parallel to v = F dot v / |v|
|v| = sqrt{10}
v = -i - 3j
F = -15j
F dot v = (-3)(-15) = +45
F dot v / |v| = 45 / sqrt{10}
make sure you can enter in square roots, or if it wants decimals only, and how they want you to round it.
----
If that is the exact problem text, that was not clear phrasing. People say component to mean magnitude, and vector to mean vector. Anyway,
So we agree the projection is 45 / sqrt{10}, this is a projection parallel to v, you can write any vector as
vector = (magnitude)(unit vector)
so the vector we want is constructed from
(magnitude) = 45 / sqrt{10}
unit vector = v / |v| = (1/sqrt{10}) (-i - 3j) <--- we use v because we found a projection *parallel* to v, the force acts in this direction too then by construction.
F_parallel = (45 / sqrt{10} ) (1 / sqrt{10} ) (-i - 3j) = (45/10)(-i - 3j).......[Ans.]
Your online submission system probably wants you to multiply 45/10 through and may not like the factored form above, just as a forewarning.