Vectors Sections 6 6 Objectives Rewrite a vector

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

Formulas • Rectangular Coordinate a vector v with initial point and terminal point can be represented in rectangular coordinates as • 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.

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

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

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

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

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

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

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 °.