Orthogonal, Parallel, or Neither (TL 20)
Are〈2, 3〉and〈-6, 4〉orthogonal?
Yes, dot product is 0
Find the angle between the vectors a = ⟨1, 0⟩, b = ⟨0, 1⟩
90°
Given a = ⟨1, 0⟩ and b = ⟨7, 5⟩, what is the projection of b onto a?
<7, 0>
If the dot product is positive, the angle between vectors must be…
acute
Find k if a =〈k, 3〉and b =〈4, 8〉are orthogonal
-6
List Three unit Vectors that are orthogonal to each other.
possible answer: e1, e2, e3
What is the scalar projection of b =〈3, 4〉onto a =〈5, 0〉?
<3, 0>
If |u| = 4 and |v| = 7, what is the maximum possible value of u • v? (hint: what is the max value of cosine)
28
What is the dot product of two parallel vectors (Pointing in the same direction) with magnitudes 3 and 7?
21
Find the angle between the vectors a = ⟨2, 1⟩, b = ⟨1, 2⟩
36.9°, cos-1(⅘), 0.644
Find the vector projection of b = ⟨4, 2⟩ onto a = ⟨1, 1⟩.
⟨3, 3⟩
If you double the length of vector a, what will happen to dot product a • b?
It will double
Determine the value of c such that the vectors a = 〈4, -6〉and b = 〈c, 9〉are parallel
c = -6
Find the angle between the vectors a = i + 2j -2k, b = 4i - 3k
48.2°, cos-1(⅔), 0.841
Find the projection of b = 〈-1, 4, 8〉onto a = 〈2, 1, 2〉
<4,2,4>
Find the magnitude of the vector a = 3i + 5j
sqrt(34)
If u and v are unit vectors and they are orthogonal, what is the magnitude of their sum, |u+v|?
sqrt(2)
A force vector acts as F = ⟨3, -2, 6⟩ and a displacement vector is d = ⟨1, 4, -2⟩. Find the angle between these two vectors.
122.0°, cos-1(-17721), 2.13
Find the vector projection of b = ⟨3, -2, 5⟩ onto a = ⟨2, 1, -2⟩. Simplify your answer completely.
⟨-4/3, -⅔, 4/3⟩
Linear Combination