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Dot Product

Vector multiplication operation in which you multiply corresponding components of two vectors and add them to products of other corresponding components.

Sqrt(V1^2+V2^2+...+Vn^2)

Length (of a vector)

Magnitude/Norm

Length of a vector

Unit Vector

Vector with length 1

Cauchy Schwarz Inequality

For any two nonzero vectors in R^n, the absolute value of their dot product is less than or equal to the product of the lengths of the vectors

Triangle Inequality

For any two nonzero vectors in R^n, the length of the sum of the two vectors is less than or equal to the sum of the lengths of each of the vectors

Law of Cosines

C^2 = A^2 + B^2 - 2ABcos@

Perpendicular

A wave in which the vibration of the medium is _______ to the direction in which the wave travels is called a transverse wave.

Orthogonal

The dot product of two vectors is 0

Normal vector (to a plane)

A vector that is perpendicular to plane in question

Right Hand Rule

Fingers - Direction of magnetic field (B)

Vector quantity

9.8m/s per second is a

vector

a displacement distinguished by magnitude and direction but not by location.

Magnitude...

... of a vector is always a positive quantity

equal vectors

have same direction and magnitude

vector sum A +B

place the initial point of vector B at the terminal point of vector A, the vector with the same initial point as A and the same terminal point as B is the sum; the…

parallelogram rul

another method to find A = B; place vectors A and B so that their initial points coincide, then complete a parallelogram that has A and B as two adjacent sides; the diagonal of…

opposite vector

a vector with the same magnitude as the original, but opposite direction.

zero vector

a vector of length zero.

scalar product

a real number(scalar) k and a vector u create the vector u create ku, which has magnitude |K| times the magnitude of u; ku has the same direction as us if k>0, and the opposite direction if k<0

position vector

a vector with its initial point at the origin; with its endpoint at (a, b) is written <a, b,> so u=<a,b>

direction angle

the positive angle between the x axis and a position vector

8

Find u · v if u = ?4,0? and v = ?2,1?.

-16

Find u · v if u = -3i + j and v = 5i - j.

56

Find u · v if u = ?8, 2? and v = ?6, 4?.

-23

Find u · v if u = 2i - 5j and v = 6i + 7j.

73

Find u · v if u = ?4, 25? and v = ?-13, 5?.

48.752

Find the angle between the following vectors if u = 5i + 7j and v = 10i + j (to the nearest thousandth).

56.575

Find the angle between the following vectors if u = ?9, 4? and v = ?2, 12? (to the nearest thousandth).

8.130

Find the angle between the following vectors if u = 3i + 5j and v = 8i + 19j (to the nearest thousandth).

99.232

Find the angle between the following vectors if u = ?20, 1? and v = ?-3, 14? (to the nearest thousandth).

129.822

Find the angle between the following vectors if u = -23i + 6j and v = 8i - 17j (to the nearest thousandth).