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8.5
Vectors
more examples
Given v = 3i + 6j and w = -2i + 3j
Find the decomposition of v into two vectors
that are perpendicular to each other.
v1 = ( v • w / ll w ll2) * (w)
v1 = 12 / 13 (w) = (-24/13) i + (36/13)j
v2 = v – v1 = (51/13) i + (42/13) j
Word problems:
A DC 10 jumbo jet maintains an airspeed of
550 miles per hour in a southwesterly
direction. The velocity of the jet steam is a
constant 80 mph from the west. Find the
actual speed and direction of the aircraft.
Ex 2
A Toyota Sienna weight of 5300 pounds is
parked on a street with a slope of 8º. Find
the force required to keep the Sienna from
rolling down the hill. What is the force
perpendicular to the hill?
An airplane has airspeed of 600 km/hr
bearing S30E.The wind velocity is 40
km/hr in the direction of S45E. Find the
resultant vector representing the path of
the plane relative to the ground. What is
the ground speed of the plane? What is its
direction?
HW pg 637 20 – 28 even