1) Determine the angle between vectors:
U = <2, -3, 4> and V= <-1, 3, -2>
2) determine the distance between line and point
P: -2x+3y-4z =2
L: 3x – 5y+z =1
3) Determine the distance between the line L and the point A
given by
L; (x-1)/2 = (y+2)/5 = (z-3)/4 and A (1, -1,1)
4) Find an equation of the line given by the points A, B and
C.
A (2, -1,0), B (-2,4,-1) and C ( 3,-4,1)...
Suppose that vectors x and y are such that
IxI=3 and IyI=4, and the angle between x
and y is 71°. Solve the triangle determined by
the vectors 3x , y, and I3x - y
I. That is, report all side lengths and angles in this triangle to
3 decimal places accuracy.
Are the vectors v1 = (1 , 2, 3), v2 = (2, 4, 6), and v3 = (1, 1,
3) linearly independent or dependent? Since v2 is a scalar multiple
of v1, both v1 and v2 are linearly dependent, but what does that
say about the linear dependence of the three vectors as a
whole?
6.
Used for loop, create a table that convert angle values from
degrees to radians, from 0 to 180 degrees, in increments of 4.
7. Apply the same operation using the vectorization
Find the distances:
A) Between ?1=〈2+2?,−1+?,−3?〉and ?2=〈4,−5−3?,1+4?〉 .
B) Between the planes 2?−?+5?=0 and 2?−?+5?=5 .
C) From the point (1,2,3) to the line ?=〈−?,4−?,1+4?〉 .
The payoff matrix for a game is 4 −1 5 −6 2 1 1 −4 2 . (a) Find
the expected payoff to the row player if the row player R uses the
maximin pure strategy and the column C player uses the minimax pure
strategy. (b) Find the expected payoff to the row player if R uses
the maximin strategy 40% of the time and chooses each of the other
two rows 30% of the time while C uses...
Convert 6∘ to radians,
correct to 4 decimal places.
6∘= ____________ rad
(4 dec. places).
Convert 4.75 rad to
degrees, correct to 4 decimal places.
4.75 rad =
____________ degrees (4 dec. places).
Question b: (2 points)
Determine the length
of an arc of a circle with radius 6 metres that subtends a central
angle of 300∘ to two decimal places.
Arc length,
s= ____________ m.
c A circular wheel of
radius 0.55 metres is spinning at a rate of...