Warm up: Vector Components
• An airplane is traveling upwards at a 30
degree angle with a velocity of 500 km / hr.
• How fast is it moving horizontally?
Projections of Vectors
Section 7.5
Scalar Projections of Vectors
• A vector projection is a perpendicular
projection of one vector onto another
• How would you find the magnitude of the
projection of u onto v?
Reasoning with Projections
• If vector a = (2, 3)
and vector b = (5, 0),
then find the
magnitude of:
a)The projection of a
onto b:
Reasoning with Projections
• If vector a = (2, 3)
and vector b = (5, 0),
then find the
magnitude of:
a)The projection of a
onto b:
b)The projection of b
onto a:
Directions of Vectors
In three dimensions, we
can find the direction of
each vector in relation to
the x, y and z axis.
Find the angle between:
a) OP and the x axis
Directions of Vectors
In three dimensions, we can
find the direction of each
vector in relation to the x,
y and z axis.
Find the angle between:
a) OP and the x axis
b)OP and the y axis
c) OP and the z axis
Vector Projections
• The vector a (3, 4) is
projected onto the
vector b (5, 0).
• What is a vector in the
direction of b whose
magnitude is the
magnitude of projba:
Summary
• How do you calculate the projection of a onto b?
How do you calculate the projection of b onto a?
• What is a direction cosine?
• What is the difference between a vector
projection and a scalar projection?
• Practice: Pg. 398, #1, 4, 7, 13,