Determinants
Compute the 2×2 determinant:
|2 1; 3 4|
5
Find the area of the parallelogram formed by
a = ⟨3, 0, 0⟩ and b = ⟨0, 2, 0⟩
6
The vector a x b is orthogonal to _____
a and b
What is the general formula for finding the magnitude of the cross product of two vectors a and b with angle θ between them?
|a|.|b| sin(θ)
Find a × b using the determinant method where
a = ⟨1, 2, 0⟩ and b = ⟨0, 1, 3⟩
a × b = ⟨6, −3, 1⟩
Find the area of the parallelogram formed by
a = ⟨1, 2, 0⟩ and b = ⟨0, 1, 3⟩
√46
Find a vector orthogonal to both
A =⟨2,1,3⟩
B =⟨1,-2,4⟩.
⟨10,-5,-5⟩ or ⟨2,-1,-1⟩
What will be the cross product of the vectors 2i + 3j + k and 6i + 9j + 3k?
0
A =⟨2,−1,3⟩
B =⟨4,0,−2⟩.
Use a determinate to calculate A × B.
⟨2,16,4⟩
Find the area of the triangle with vertices
P(1,0,0), Q(0,2,0), R(0,0,3)
7/2
Find a unit vector orthogonal to both:
a =⟨2,−1,0⟩ And b=⟨1,3,4⟩
⟨-4,-8,7⟩ / sqrt(129)
Determine whether
a = ⟨1,2,−1⟩, b = ⟨2,−1,4⟩, and c = ⟨3,3,2⟩
are coplanar and explain.
They are not coplanar because the scalar triple product is not equal to zero.
Let m =⟨5,−2,1⟩ and n = ⟨2,4,−3⟩.
Compute m × n using determinants.
⟨2,17,24⟩
Find the volume of the parallelepiped determined by
a = ⟨6,3,−1⟩, b = ⟨0,1,2⟩, c = ⟨4,−2,5⟩
58
Find all values of k such that ⟨1,k,2⟩×⟨3,1,−1⟩ is orthogonal to ⟨2,4,1⟩
k = 5
Find the angle between ⟨1,2,3⟩ and ⟨4,−1,2⟩ using the magnitude of the cross product.
approximately 62.2 degrees.