C4- Vectors Flashcards
What is a vector?
A quantity with direction and magnitude
When are vectors equal?
When the direction and magnitude are the same
How do you find the magnitude of xi+yj+zk?
√(x^2 +y^2 +z^2)
This is also the distance from the origin to the point
How do you denote a vector that’s parallel to vector A?
λA, where λ is a non-zero scalar
What is a unit vector?
A vector that has a magnitude of 1 unit
Which letter is used for the unit vector that’s parallel to the x-axis?
i
Which letter is used for the unit vector that’s parallel to the y-axis?
j
Which letter is used for the unit vector that’s parallel to the z-axis?
k
If λa + μb = αa + βb, and a and b aren’t parallel, then
λ=α
μ=β
How do you find the distance between the two points, (x1,y1,z1) and (x2,y2,z2)?
√((x1-x2)^2 + (y1-y2)^2 + (z1-z2)^2)
What is the dot product of vectors a and b, if a=(a1i,a2j,a3k) and b= (b1i,b2j,b3k)?
a.b= (a1b1) + (a2b2) + (a3b3)
What is the dot product of a and b also equal to?
a.b= (|a||b|)cosθ
If a and b are perpendicular, what does a.b equal?
0
If a and b are parallel, what does a.b equal?
|a||b|
What is the vector equation of the vector that passes through A, with position vector a, and is parallel to the vector b?
r=a+ λb
Where λ is a scalar parameter
