Calculate the scalar triple product u · (v x w), where u = (7,7,0), v = (-3,–9,7), and w = (7,–9, 1). (Use symbolic notation and fractions where needed.) u · (v x w) =

Q: Let x→=8i→−11j→ and y→=4j→−9k→  be two vectors. Find the value of the scalar product x→⋅y→.

A: We have to find the scalar product

Q: Find the scalar product a•b when (i) a= x+2y -z and b=2x+3y +z (ii) a=x-3y +z and b=2x+y +z

A: We have to find the scalar product a·b when (i). a=x+2y-z and b=2x+3y+z(ii). a=x-3y+z and b=2x+y+z

Q: Compute the orthogonal projection of u onto v. Use the square root symbol 'V' where needed to give…

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Q: Evaluate f a'y*da + =*ydy counterclockwise around the square with vertices (0,0), (1,0), (1,1), and…

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Q: Consider the following function. T: M, 2+ R, T(A) = a – b – c – d, where A = Find the following…

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Q: Find the constants c1 and c2, such that vector = c1 +c2

A: In this question, we have to find the value of constant c1 and c2 for the given condition  with…

Q: Use the scalar triple product to detemine whether the points A(1, 3, 2), B(3.-1.6), C(5, 2, 0), and…

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Q: Use the scalar triple product to determine whether the points A(1, 3, 2), B(3, -1, 6), C(5, 2, 0),…

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Q: Let U(7, 6, -5), V(2, 8, -2), and W(1, 10, o). calculate the scalar triple product U.(VxW) Answer:

A: Given that  The vectors U(7,6,-5) V(2,8,-2) and W(1,10,0) To find the U(V*W)

Q: Calculate the scalar triple product u · (v × w), where u =〈1, 1, 0〉, v =〈3, −2, 2〉, and w =〈4, −1,…

A: The vectors are, u=1,1,0v=3,-2,2w=4,-1,2 We need to find the scalar triple product u·v×w

Q: Determine whether v and w are orthogonal given v=-5i+2j and w=2i-4j

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Q: Let u = 2i - j, v = 3i + j, and w = i + 4j. Find the specified scalar 5(v . w)

A: Given vectors are: u=2i-jv=3i+j and, w=i+4j We have to find the value of 5v.w Here we have to use…

Q: v = 8i – 5j – 4k - w = -5i + 9j – 4k Compute the dot product v w.

A: The formula for dot product of two vector a→=a1i^+a2j^+a3k^ and b→=b1i^+b2j^+b3k^ is given by the…

Q: Let v = (– 1, 19, 19) and w = (– 27, – 7, – 47) be ordered triples in R'. Find two scalars ci and C2…

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Q: let u =8i-4j, v=i-j, w=i+j. Find the scalars a and b such that u = av +bw

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Q: Q.4.(a). Show that the following functions is not an inner product on R3, where u = (u, U2, U3) and…

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Q: Find the triple scalar product (u x v) w of u= 4i+ 2j- j, v=8i +5j- 4 k w= 5 i + 10 j - 9 k 102 29…

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Q: If Lo and Li are parallel, then vo = is a scalar multiple of vi = . اختر احدى الدجابات

A: If two lines  L0: (x,yz)=(x0+a0t, y0+b0t, z0+c0t)And,L1:(x,y,z)=(x1+ sa1, y1+sb1, z1+sc1) Are are…

Q: Describe the additive inverse of a vector, (Vị, V2, V3), in the vector space. R3 O (-v1, -V2, -V3) O…

A: The additive inverse means  the value of the vector  when added to the original vector  gives the…

Q: The dot product of u = (3, 5, 2) and v = is equal to the scalar product of p = 31 - 5j + 2k and q =…

A: The component representation of a vector u=ai+bj+ck is  u=<a, b, c>. So the vectors u and v…

Q: Solve the problem. Let u = 5 i + j, v = i+ j, and w = i- j. Find scalars a and b such that u = a v +…

A: Given: u=5i+j, v=i+j, w=i-j and u=av+bw   To determine: The scalers a and b such that u=av+bw

Q: Use the inner product (u, v) = u,V1 2u2V2 to find (u, v). + u = (6i, -i) and v = (i, 7i) (u, v) =

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Q: Suppose u = (5, 3,0), v = (0, 3, 9), and w = (-1, –9, –3). Compute the three triple scalar products…

A: We will solve the following.

Q: let v =〈−2, 5〉and w =〈3, −2〉. Find a scalar α such that ||v + αw|| = 6.

A: Given, v=-2, 5w=3, -22

Q: Determine the real number a such that u X v| and i are orthogonal, where u = 2i + 4j + 3k and v = 8i…

A: u=2i+4j+3kv=8i-10j+αk

Q: V = R' = {(x.y)|x, y e R}, with standard operation of addition on R² which is (x,.y,)+(x,, y2) = (x1…

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Q: Determine whether v and w are parallel, orthogonal, or neither. v=-2i+3j, w=-4i+6j

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Q: Use the vectors u = (5, 5) and v = (-6, 1) to find the indicated quanti (u v)v (u v)v = State…

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Q: Compute the dot product u. V. 02 08 5,V= 0-8 3

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Q: Find the cosine of the angle between the vectors P1 (x) = 1 + 2xr – x² and p2 (x) = -2 – 3x + 2x² -…

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Q: Determine whether the statement is true or false. If a, is divergent, then la,I is divergent. True…

A: To determine whether the statement is true or false. If ∑nan is divergent, then ∑nan is divergent.

Q: Use the scalar triple product to determine whether the points A(1, 3, 2), B(3, – 1, 6), C(5, 2, 0),…

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Q: Find the triple scalar product (u xv) •w of the given vectors. u= - 5i – 3j + 4k v = 9i – 10j + 7k w…

A: Given that      u = -5i-3j+4k     v = 9i-10j+7k     w = 9i-7j-3k Here we have to find the value of…

Q: Determine the real number a such that u x v and i are orthogonal, where u = 5i + j - 9k and v = 6i -…

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Q: Use the inner product (f, 9) = f(2)g(=) dæ in the vector space P(R) of polynomials to find (f, 9),…

A: The inner product is f, g=∫01 f(x)g(x) dx The functions given are f(x)=10x2-3 and g(x)=-9x+10

Q: Let r (t) = The dot product r (1) · r ' (1) =

A: First differentiate at given value then take dot product

Q: Use the quotient law for tensors to show that the array -2xy -2xz /y²+z²-x² -2yx x²+z²-y² -2yz -2zx…

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Q: Suppose a is a non-zero scalar, v = (a, 2a, –a), and w = which of the following equals (2v) × (-4w)?…

A: Cross product

Q: Let Z= (3 – 4i)(4+ 5i), Find the conjugate of Z. %3D 28 + 4i 32 +i 28 – 4i 34 – 2i 32 – i

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Q: Let Define addition and scalar multiplication as follows. b +e) Ic+f kby verify the following…

A: Given vector is: V=1bc1 b, c∈RThe addition and scalar multiplication are defined…

Q: Let u = 8i + 2j, v=i+j, and w =i-j. Find scalars a and b such that u = av + bw. a = b =

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Q: Use coordinate vectors to test the linear independence of the set of polynomials {1– 212 –t',t+21,…

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Q: Let u = 2i - j, v = 4i + j, and w = i + 7j. Find the specified scalar. u•v+u•w +u•w= (Simplify your…

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Q: Let v = (60, – 5, – 5) and w = (– 4, – 30, 22) be ordered triples in R°. Find two scalars c and such…

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Q: Find the cosine of the angle between the vectors P1 (x) = 1 + 2x – x2 and p2 (x) = -2 3x + 2x? %3D -…

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Q: Let u = 2i - j, v = 3i + j, and w = i + 4j.Find specified scalar 5(v . w).

A: Since, we have been given that:-u=2i-jv=3i+jand w=i+4jOur Aim is to find the specified scalar…

Q: Prove the triple scalar product identity A ⋅ (B x C) = (A x B) ⋅ C.

A: Concept: A rectangular array of numbers (or other mathematical objects) for those the operations…

Q: The dot product of u = ⟨u1, u2⟩ and v = ⟨v1, v2⟩ is u ∙ v = ________.

A: Dot Product: The vector is u=(u1,u2)v=(v1,v2)u=u1i+u2jv=v1i+v2j