Vectors Sections 6.6

Objectives Rewrite a vector in rectangular coordinates (in terms of i and j) given the initial and terminal points of the vector. Determine the magnitude and direction of a vector given in terms if i and j. Add and subtract vectors given in terms of i and j. Multiply a vector given in terms of i and j by a real number (scalar multiplication). Find a unit vector for a vector given in terms of i and j. Write a vector in terms of i and j the magnitude and direction of the vector.

Vocabulary vector scalars scalar multiplication unit vectors magnitude

a vector v with initial point and terminal point can be represented in rectangular coordinates as Formulas Rectangular Coordinate Magnitude a vector v with initial point and terminal point has a magnitude of

Write the vector v with initial point P 1 = (2, —9) and terminal point P 2 = (5, —6) in rectangular coordinates.

Write the vector v with initial point P 1 = (3, 6) and terminal point P 2 = (3, —1) in rectangular coordinates.

a vector v with magnitude ||v|| and direction θ can be written Write a Vector in Terms of Its Magnitude and Direction

Find the magnitude and direction of the vector u = 8i — j.

Find the magnitude and direction of the vector v = 1i + 2j.

Given the vectors u = —3i — 7j and v = 10i — 8j, find ||u|| u + v u — v 4v 10u + 7v

the unit vector of v is a vector of magnitude 1 that has the same direction as the vector v Definition and Formulas Unit Vector

Find the unit vector of the vector v = — 1i — 2j.

Write the vector v in terms of the i and j components if ||v|| = 3 and θ = 60 °.

Write the vector v in terms of the i and j components if ||v|| = 5 and θ = 225 °.

Write the vector v in terms of the i and j components if ||v|| = 5 and θ = 180 °.