Given the ordered basis 1 B = {m₁ = [ ¹7 ] , ¹₂ = [-2]} find [v]B, the coordinates of v = [ -5 -23 [V]B Ex: 5 with respect to B.

Q: Given u = (4, -2) and v = 3i + 5j. Find u + v, v - 2u, and -6u + 5v in component form.

A: ai + bj + ci + dj = (a+c)i+ ( b+d)j

Q: Let u = , v = , and w = . find uw

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Q: Let i = [-1 4] and j = [-4 1]. Find the following vectors. i = 62 i = -6j = | w = 62 – 6ỹ = = [ -

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Q: Let u = PQ and v = PR ; where P = (2, – 1, 3) Q = (0,5, 1) and R = (5,5,0) find a. The component…

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Q: Use the vectors v=3i+j-2k and w=-3i+2j-k to find each expression. ||v - w ||

A: Given vectors are: v=3i+j-2kw=-3i+2j-k We have to find v-w.

Q: Find the point P such that v = PQ has the components (-7.75, –8.25, – 16). О 3D (-2.75, -2.25, -6) P…

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Q: Determine whether v = 3i - 5j and w = 6i - 10j are parallel,orthogonal, or neither.

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Q: Find an expression for the exact angle 0 between u and v when = (4,7) and v = (-5, 8). (3, –1, 1)…

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Q: Let i = [1 -4] and y = [4 -6]. Find the following vectors. i = 57 ü = 2g =| w = 5i + 2j =||

A: The solution is given below:-

Q: 47. ā -b = -8

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Q: Determine whether v = -2i + 3j, w = -6i - 9j are parallel, orthogonal, or neither.

A: Determine whether v=-2i+3j,  w=-6i-9j are parallel, orthogonal, or neither. Solution:- if two…

Q: 2.30 Let r denote a position vector r = x= xê, (r² vector. Use index notation to show that: (a) ²…

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Q: Given u⃗ =⟨2,−5⟩ and v⃗ =⟨4,−4⟩, find the dot product u⃗

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