Chapter 3: Vectors Flashcards
What is a scalar quantity?
A quantity described by a numerical value but without an associated direction.
What is a vector quantity?
A quantity with both size (magnitude) and direction.
How is the magnitude of a vector denoted?
|a| (With an arrow above the vector’s symbol)
What is a unit vector?
A dimensionless symbol with a magnitude equal to one, with the purpose of specifying a chosen direction.
The unit vector ___ points in the +x direction.
î
The unit vector ___ points in the +y direction.
ĵ
The unit vector ___ points in the +z direction.
k̂
r(arrow) = …
a(arrow) + b(arrow) + c(arrow)
The r(arrow) equation above can be used to deal individually with ___ components.
x, y, and z
TRUE or FALSE: Components must be dealt with separately (IE, y’s with y’s, x’s with x’s, and so on).
True!
What is the definition of a scalar product?
a(arrow) * b(arrow) = |a(arrow)||b(arrow)|cosΦ
The right side of the scalar product equation contains only scalars. Thus, the product produces a ___.
Scalar
The scalar in a dot product can be either positive or negative depending on the sign of cosΦ, but the sign (does)/(does not) indicate a direction.
Does not
You (can)/(cannot) use the larger angle between the vectors, as it (does)/(does not) have the same result.
Can; does
The product is also called the “dot product” because of the center dot, and is spoken as ___ or ___.
“a dot b”; “a dotted into b”
The scalar product in unit-vector notation simplifies down into:
a(arrow) * b(arrow) = a(subx)b(subx) + a(suby)b(suby) + a(subz)b(subz)
A vector cross-product is written as…
a × b
When doing a cross product, (a is collapsed into b)/(b is collapsed into a).
Vector a is collapsed into vector b.
The direction of c, the resulting vector, is determined using the ___.
RHR, or right-hand rule.
The vector product of cross products (is)/(is not) communicative.
Is not.
