2. Let x and y be vectors in R³. Prove that y=(|x +ỷ1² − |x|² − |ÿ1²): a) Using a geometric approach. b) Using an algebraic approach (i.e. using components)

Q: Let u = 4i + 5j, v = -4i +2j, and w = 3i - j. Determine the i, j form of each of the following: (a)…

A: “Since you have posted a question with multiple sub parts, we will provide the solution only to the…

Q: Let V = (image) the space of symmetric real 2×2 matrices. Consider T : V → R2 defined by T(image).…

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Q: Compute (u v Ղա • Ա. . — u = (i, 7,6), v = (2, -7i, 1+i), w = (7-i, 7i, 3 + 6i) u · v) ա • Ա —

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Q: Write v as the sum of two vector components if v = i +3j and w = 2i+j. O v = (-2i+2j) + (i +j) Ov=…

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Q: 3. Which vector is not equal to zero? a) ix (j×k) b) (ix j) × k c) (i × i) × j d) ix (ix j)

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Q: 3. Add the vectors shown.

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Q: The vectors į+j and i-į are perpendicular. True False

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Q: Define x and y as vectors x = 2,4, 6,8, 10 and y = 3,6, 9, 12, 15 (Use shortcuts if applicable).…

A: Given that, x=2,4,6,8,10y=3,6,9,12,15z=xy+yx(x+y)+12xy

Q: Let v = 2i - 5j and w = -4i + 3j. Find v . w

A: We have to find the dot product value v.w for given vectors: v=2i-5j and w=-4i+3j We know that for…

Q: let v =〈−2, 5〉and w =〈3, −2〉. Sketch v, w, and 2v − 3w.

A: Given vector:                   v=-2,5 and  w=3,-2   Algebra of vectors: Let v = x1, y1 and w =  x2,…

Q: Quolel X= -gi +sj -K, Y. i-2 k yo i-2 K Find X x Y

A: (1) Consider the given vectors x=-2i+3j-k and y=i-2k   We have to find x×y   Now, x×y=ijk-2   3-11 0…

Q: Find the vector expression for the line that is the intersection of the planes 3x−3y−2z=−2 and…

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Q: Let V/1 ----- For what value of h is y in the span of the vectors v1 and v₂? h

A: Let, v1=15-4,  v2=-3-168, y=843h To determine the value of h in the span of the vectors v1 and v2.…

Q: Let -81 2 V1 = V2 = 18 23 -2 -3 h For what value of h is y in the span of the vectors v1 and v2? h =

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