Consider vectors, 2 u = |2, v = w = |-3 (a) Do these vectors line in a plane ? Why? Why not? Find the coefficients for linear combinations if exist.

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Chapter5: Inner Product Spaces
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Consider vectors,
u = |2, v =
l3]
w = |-3
(a) Do these vectors line in a plane ? Why? Why not? Find the coefficients for linear
combinations if exist.
(b) Find ||u + 배 and ||v-에.
(c) Find the unit vectors au, ap, a, in the direction of the vectors u, v, w respectively.
(d) Confirm the Cauchy-Schwarz inequality for u, v and confirm the triangle
inequality for v, w.
(e) Find the angle between u, and v.
Transcribed Image Text:Consider vectors, u = |2, v = l3] w = |-3 (a) Do these vectors line in a plane ? Why? Why not? Find the coefficients for linear combinations if exist. (b) Find ||u + 배 and ||v-에. (c) Find the unit vectors au, ap, a, in the direction of the vectors u, v, w respectively. (d) Confirm the Cauchy-Schwarz inequality for u, v and confirm the triangle inequality for v, w. (e) Find the angle between u, and v.
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