Y2, C12 - Vectors Flashcards
How do you find the distance from the origin to a 3D point
root(x^2 + y^2 + z^2)
How do you find the distance between two 3D points
root(∆x^2 + ∆y^2 + ∆z^2)
For position vectors a and b, what is the formula for AB
AB = OB - OA
AB = b - a
What is the formula for unit vector (e.g. unit vector of (2i, -j, 4k)
Unit vector = vector / magnitude of vector
= (2i, -j, 4k) * 1 / root(16 + 4 + 1)
= (2i, -j, 4k) / root(21)
What does it mean if vectors are parallel
They are factors of each other
What is the formula for the angle between a = (x, y, z) and the x-axis, y-axis, and z-axis
cos(thetax) = x / lal
cos(thetay) = y / lal
cos(thetaz) = z / lal
Find the angle a = 2i - 3j - k makes with the y-axis
cos(x) = y / lal
cos(x) = -3 / root(14)
x = 143.3 degrees
Given position vectors A and B, how would you show that OAB is isosceles
Find magnitude of AB and see if it is equal to magnitude of OA or magnitude of OB
What does collinear mean
The points line on the same straight line
If you know the points Q, P, R, how would you find the point S to form a parallelogram PQRS
Draw it out (S must be between P and R)
QP = RS
Find QP
RS = s - r = QP
s = QP + r
Sub in values to find s
How do you prove that 2 diagonals bisect at a point
Find 2 different routes to the point using mu’s and lambda’s and compare coefficients of the ways the routes got there (e.g. coefficients of a’s and b’s)
What is the scalar of the vector force (3i, 4j, -k)
root(26) N
What is the scalar of the displacement (12i, 3j, 4k)
13 m
How do you find the scalar of a vector quantity
Find the magnitude
How would you find the resultant force acting on a particle if it is being acted on by 3 forces
Add the forces
