Vectors Flashcards
What do you need to get the equation of a plane?
The normal to the plane and a point on the plane.
How would you prove that 3 planes have a solution (intersect at a point) without actually solving for that point?
Prove that the determinant is non singular (not equal to zero). Note: they may still have infinite solns - line of intersection.
If a and b are direction vectors, what do you get when when you do: a x b
A direction vector which is perpendicular to a and b.
What is the scalar cross product for direction vectors a,b and c?
a. (b x c)
What is the formula for area of a parellelpiped?
|a.(bxc)|
How do you prove that 3 lines are co-planar?
Prove that |a.(bxc)| = 0 (no volume!)
For coordinate p =(a,b,c) Write down the direction cosines
Cos α= a │p│Cos Β = b │p│Cos γ = c │p│
For the vectors a and b:when does a.b = 0
a.b = 0 when vectors a and b are perpendicular
For the vector a, what is the value of : a.a
a.a = │a│^2
For the direction vectors a and b,Write down the formula for Cos Θ
Cos Θ = a.b │a││b│
What is the equivalent of p x q?
p x q = -q x p
For direction vectors a and b:When would a x b = 0
a x b = 0 if and only if direction vectors are parallel.
What is the direction vector of the line:2x – 5 = 5-4y = z + 6 3 5 2
(3/2 i – 5/4 j + 2k)
For planes with direction vectors n1 and n2write down the formula for the angle between the 2 planes.
Cos Θ = │n1.n2│ │n1││n2│
For plane with direction vector n and line with direction vector d, write down the formula for the angle between them.
Cos Θ = │n.d│ │n││d│α = 90 - Θ
