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It is (x + yj) / |x + yj|
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What is the vector equation for the x axis?
ki where i is the unit horizontal vector, and k is any number.
Prove that the unit vector is dimenssionless?
The unit vector is the ratio of the vector and its magnitude, thus : R/r = (Ix + Jy + Kz)/r where r= Sqroot(x^2 + y^2 + z^2). Units of the vector and the magnitude are the same thus divide out and the unit vector is dimensionless.
Is torque is a scalar or a vector quantity?
Since torque is a force, and as such has a direction, it is a vector.
Does a unit vector have direction?
No it doesn't. A unit vector indicates direction only. The length of the orthogonal components are RELATIVE to the absolute length of the vector, thus cannot have a unit. For instance, let X'=X/x where X is a vector, x is a scalar and X' is a unit vector. X has length and direction and x has length only, thus X' has direction only. Here's an example. C = A + B where A=3m*A' and B=4m*B' (where A and B are orthogonal) cC' = aA' + bB' C' = (a/c)A' + (b/c)B' = xA' + yB' c = sqrt(3m^2+4m^2) = 5m (by pythagorous) x = (3m/5m) = (3/5) (notice that the units cancel out!) y = (4m/5m) = (4/5) (notice that the units cancel out!)
Can you add three unit vectors to get a unit vector does your answer change if two unit vectors are along the coordinate axes?
Yes., and their being along the coordinate axes does not change the answer.Consider the vectors: i, -i and j where i is the unit vector along the x axis and j along the y axis. The resultant of the three is j.
What is the eqution for x component in a vector?
x = V times (cos A ) where V = vector magnitude and A = angle of vector to the x plane
When should you express a vector along the x-axis as a negative vector?
You express a vector along the X-axis as a negative vector when the arrow representing the vector would point toward negative x.
What is augmented vector?
An augmented vector is a vector that is augmented with an extra dimension. This new dimension always takes on the value of 1. e.g. X = (5, 2) X' = (5, 2, 1) where X' is the augmented form of vector X.
How do you find the component of a vector perpendicular to another vector?
The component of a vector x perpendicular to the vector y is x*y*sin(A) where A is the angle between the two vectors.
Why is it impossible to add a scalar to a vector?
It is not impossible to add a scalar to a vector. e.g. e^ix = cos(x) + isin(x) when x is 0 the answer is a scalar, when x=90 degrees the answer is a vector, when x is not a multiple of 90 degrees the answer is the sum of a scalar and a vector. So it is only impossible to add a scalar to a vector when x is a multiple of 90 degrees, all other angles add a scalar to a vector.
Can scalar be a negative number?
Yes, a scalar can be a negative number. For instance: c<x₁,x₂> = <cx₁,cx₂> such that <x₁,x₂> is a vector. Let c = -1 for instance. Then, we have this vector: <-x₁,-x₂> Compared to <x₁,x₂>, <-x₁,-x₂> has negative signs. In physics and mathematics, if we multiply the vector or something by a negative value scalar, then the direction of the vector is reversed, and the magnitude stays the same. If the magnitude increases/decreases, and the direction of the vector is reversed, then we can multiply the vector by any negative non-1 scalar value.
When should you express a vector along the x axis as a negative vector?
When the arrow representing the vector would point toward negative x.
