Perform the stated operations on the given vectors u, v and w. u = 3 i − k , v = i − j + 2 k , w = 3 j a w − v b 6 u + 4 w c − v − 2 w d 4 3 u + v e − 8 v + w + 2 u f 3 w − v − w
Perform the stated operations on the given vectors u, v and w. u = 3 i − k , v = i − j + 2 k , w = 3 j a w − v b 6 u + 4 w c − v − 2 w d 4 3 u + v e − 8 v + w + 2 u f 3 w − v − w
Perform the stated operations on the given vectors u, v and w.
u
=
3
i
−
k
,
v
=
i
−
j
+
2
k
,
w
=
3
j
a
w
−
v
b
6
u
+
4
w
c
−
v
−
2
w
d
4
3
u
+
v
e
−
8
v
+
w
+
2
u
f
3
w
−
v
−
w
Quantities that have magnitude and direction but not position. Some examples of vectors are velocity, displacement, acceleration, and force. They are sometimes called Euclidean or spatial vectors.
5. Write the components of the following vectors: 5a. ˆı, 5b. −7ˆȷ, 5c. 4ˆı + 9ˆȷ, 5d. 5ˆı − 3ˆȷ.6. Write the following vectors in terms of ˆı and ˆȷ: 6a. ⟨2, 0⟩, 6b. ⟨0, −8⟩, 6c. ⟨7, 3⟩, 6d. ⟨4, −1⟩
a. Write the vector (-4,-8, 6) as a linear combination of a₁ (1, -3, -2), a₂ = (-5,–2,5) and ẩ3 = (−1,2,3). Express your answer in terms of the named vectors. Your answer
should be in the form 4ả₁ + 5ả₂ + 6ẩ3, which would be entered as 4a1 + 5a2 + 6a3.
(-4,-8, 6) =
-3a1+a2+2a3
b. Represent the vector (-4,-8,6) in terms of the ordered basis = {(1, −3,−2), (-5, -2,5),(-1,2,3)}. Your answer should be a vector of the general form .
[(-4,-8,6)] =
Find 4u, -5v, u + v, and 5u – 3v for the given vectors u and v.
u = i+j, v = i - j
4u =
-5v =
u + v =
5u - 3v =
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