If a = i - j + 5k and b = 2i - j - 3k find the vector c in the direction of a such that IcI = IbI -( magnitude)
I would appreaciate a explanation to how to tackle this Q, so I can do it myself.
Let me give it a try . . .
find the vector in the direction of such that
We want to have the same magnitude as .
Very well, let's find the magnitude (length) of
So now we know the length of .
We want to have the same direction at .
. . If has the right magnitude , we're done!
What is the magnitude of ?
. . . . . it's the wrong length
Can we change its magnitude to ? . . . Yes!
If we divide by , we have: .
. . This is a unit vector in the direction of (exactly one unit long).
To make it units long, multiply it by , and we have: .
So we have: . .
This is the vector with the direction of and the length of .
I would like to tell you something about vectors.Originally Posted by classicstrings
A vector has a direction and magnitude.These two properties are independent of each other. A vector is completely determined by its direction and magnitude.
There are two ways of representating a vector:
1)Using Cartesian co-ordinates
2)Using Polar co-ordinates
(These can be interchanged from one form to another, use the form you are comfortable with)
If two vectors have the same direction, then one can be expressed as a scalar times another.
In your question, c has a given magnitude(equal to b), and a definite direction(same as a). So, your vector c is unique.
(I think it may be help your revision, I will post more later)