TEST1/MAC2313
Page 2 of 5
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5. (5 pts.) What point (x
0
,y
0
) is seven-tenths of the way from
P = (-2,-3) to Q = (48,7) ??
The vector
v
with initial point P and terminal point Q has coordinates
<50,10> in standard position.
Consequently, the terminal point of
<x
0
,y
0
> = <-2,-3> + (7/10)<50,10> = <33,4> in standard position provides us
with the coordinates for (x
0
,y
0
).
Vector magic!!
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6. (5 pts.) Suppose
v
= <-3,-2, 1> and
w
= <-1,2,4>.
Then
v w
= (-3)(-1) + (-2)(2) + (1)(4)
=
3 - 4 + 4 = 3
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7. (5 pts.) Suppose
v
= <-3,-2, 1> and
w
= <-2,2,1>.
Then
v
×
w
= <-3,-2, 1> × <-2,2,1> = < -4, -(-1), -10>
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8. (5 pts.) Suppose
v
= <-3,-2, 1> and
w
= <-1,2,4>.
Then
proj
w
(
v
) = <-1/7,2/7,4/7>
, and the component of
v
perpendicular to
w
is
w
2
=
<-20/7,-16/7,3/7>
.
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