Q2.7 You have been given the following statements. Which of them are always in R? TherC uiay be more tuan true for vectors oue rigut answet. O IF u. (vx w) =4 の(7u+v)× Cu-2v)= -13Cuxv) If. u IlWI Vt IIvIl w tueu W•CV xu) =-4 is. orthoganol to v Qnd w then is also or thogonal to

Q: Let u, v, w be vectors. Which of the followings are meaningless? (Hint: The notation x means cross…

A: Use the actual meaning of vector and dot products.

Q: If u and are the vectors below, find the vector w whose tail is at the point halfway from the tip of…

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Q: Suppose ū = (2, 2) and ī = (8, –4) are two vectors that form the sides of a parallelogram. Then the…

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Q: If v = –i + 2j and --Projw= w = -2i + 3k, then - اخترأحد الخيارات -9 52+ j.A C 2 .B - C. Zero vector…

A: Solution

Q: A vector u is a positive multiple of . Vector v = with a , what will be the signs of d, e, and f?…

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Q: 7. Let -4 4 a. How many vectors are in {V1, V2, V3}? b. How many vectors are in Col A? c. Is p in…

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Q: For any three vectors a, b, and c, we have a x (b x c) (a x b) x c. اختر احدى الدجابات True False

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Q: Determine if the vector 2 b -A = 3 5 can be written as a linear combination of the vectors ---- 1…

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Q: A vector is written as aî + bĵ. What form is that?

A: A vector is written as aî + bĵ.

Q: Suppose that u, v, and w are vectors such that = 3, = -2, = 5, llull Evaluate the following…

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Q: Let = ondu= a. Compute (ul. b. Compute +7. c. Compute 3u- 2 d. Compute e. Find o vector…

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Q: Find vectors v and w so that v+w= (4,5,6) and v-w=(2,5,8). This is a question with____ unknown…

A: Addition of vectors

Q: 6. Let P, Q, and R be points in space that do not fall on the same line, and let u = PQ and v = PR.…

A: Triangle law of addition of two vectors

Q: The vectors (2,10, 4) and (1, 3, x) are orthogonal if and only if x= -8. Ignore "Give your reasons"…

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Q: Given that 7 write 3 5 7 3 5 -2 2 3 7 -1 2 2 3 3 125 100 010 -5 001 3 as a linear combination of the…

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Q: e) Let C be a new base of R3. If the base change matrix, from base A to base C is - 10 55 32 35 -5 3…

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Q: Suppose that A = V= 8 2 -1 W = 3 1 19 -1 - 10 75 – 4 −1 1 Every vector in Nul A can be written in…

A: Please see the below picture for detailed solution.

Q: Consider the vectors U₁ of R3. The vector v = {U₁, U₂} if x is: 10 O 3 02 O None of these X 8 Select…

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Q: Suppose a vector w R³ can be written as w = 5v₁ - 3v2 + 7v3, where V₁, V2, V3 are vectors in R³.…

A: Explanation of the answer is as follows

Q: 11. Find the rate.cf.changf.f.at.P.in.the directod then.vectoe ūf a. f.=ylnx. P(1,-3. --3 P.(I,-3..…

A: Directional derivative

Q: 2. Let A = a₁ + a2j + a3k and B = b₁i + b₂j + b3k. Then (A × B) . j is equal to a) a2bვ — a3b2 b)…

A: A=a1i+a2j+a3k B=b1i+b2j+b3k.

Q: "Given that 3 -4 = 5 -3+ 2 5 ܐ write 3 as a linear combination of the vectors -2 + 5 -3 -2 5 -4 1 2…

A: Here , a vector is given and now we have to represent it as a linear combination of three vectors .

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: given the followinf vectors, find |u+w| u= -3i+6j w=-2i-5j a- sqrt26 b- sqrt24 c-  -sqrt24 d- 5

A: The vectors u=-3i+6j and w=-2i-5j. Then we have to find u+w.

Q: 2. a. In each part express the vector as a linear combination of 2+x+4x², p₂ = 1 − x + 3x², and p3 =…

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Q: draw the vector -u+ 2v + 4w

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