5. Use your knowledge of vector dot product to explain why the following product is either true or false for i = (u, uz, Uz) and = (v,,v2, v3) %3D %3D u v = vu1+ vzuz + vzUg %3D

Q: Find the of A ABC Where the area vectors AC1,-1,1), B(2,1,1) and are cl-1,1, 2).

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Q: What can be said about the vectors u and v when the projection of u onto v equals u?

A: What can be said about the vectors u and v when the eprojection of u onto v equals u?

Q: Explain why u + v • w _is not defined, where u, v, and w are nonzero vectors.

A: Given 3 non zero vectors : u , v and w. We need to explain why  u + v . w is not defined.

Q: The vectors a =(1; 4; 2021) and b = (2; -8; 199) are obviously non- %3D orthogonal because the dot…

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Q: Hhewet Fint projection and Vector projiction ofBonto Afar: A-B, angte between A andBslength_of - -A=…

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Q: and (V, V2, Va) V- V = vu + VzUz + Vg3

A: The dot product between two vectors,  a→, b→ is calculated using the formula,  a→·b→= a→ b→cosθ,…

Q: u.v<0, u.w < 0 ,w .u < 0 ?

A: Given data:     The given first vector is: u. The given second vector is: v. The given third vector…

Q: The vectors a =(1; 4; 2021) and b = (2; -8; 199) are obviously non-orthogonal because the dot…

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Q: 11) Use properties of vector to determine the value of the dot product å. b for the vectors ở = 21…

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Q: The plane contains the origin and is normal to the vector&lt;4, −1, 5&gt;.

A: Given: (4, −1, 5

Q: I reached this same conclusion " Tx=Ax1x2⇒Tx=0110x1x2⇒Tx=x2x1" but had difficulty explaining it in…

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Q: Given the three vectors å ,b and ở in 3D. The following question is t termine if operation involving…

A: We can solve this as follows:

Q: Find a vector v that is perpendicular to the plane through the points А %3 (0, 4, —3), В 3 (5, —5,…

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Q: Is it true or false that the vector u = (3, 3, –3) is a direction vector to the line x + y+ 2z = 6 l…

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Q: Find the cross product a ✕ b. a = (7, 0, −2) , b = (0, 6, 0) Verify that it is orthogonal to both a…

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Q: . If u and v are nonzero vectors in Rº, why do the equa- tions u · (u x v) = 0 and v · (u x v) = 0…

A: The dot product of orthogonal vectors is equal to zero.

Q: What is the definition of the triple scalar product for vectors u, v, and w in ℝ3?

A: To Define: Scalar Triple Product for vectors u, v and w in ℝ3.

Q: 24. Verify the parallelogram law for vectors u and v in R": |u + v|l° + |[u – v||² = 2||u||² +…

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Q: Prove the stated property of distance between vectors. d(u, v) = 0 if and only if u = v

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Q: Find the vector equation for the line of intersection of the planes 5x + 2y – 5z = 2 and 5x + 4z = 4…

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Q: If A(1,2.-1) B(3.6-7), c(2,3.-3) D(3.4,-3) Calculate the angle between the vector Projection of ÄB…

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Q: 3. The dot product of two orthogonal vectors is: A.undefined. B. Zero, C. Infinity.

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Q: Find the cross product a × b. a = (4, 5, 0), b = (1, 0, 7) Verify that it is orthogonal to both a…

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Q: Explain why u + v ∙ w is not defined, where u, v, and w are nonzero vectors.

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Q: 15. Given the vector u (2i + 5j) and vector v = (3i + 4j), find the dot product u v %3D

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Q: Is it possible to have ||u−v|| = ||u + v|| if u and v are nonzero vectors? Justify your conclusion…

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Q: W,X ,Y,and  Z have the position vectors 3i+3j-4k, 4i+j+k, 2i+3k and 3i+j-4k respectively.…

A: The given position vectors areW = 3 i^ + 3 j^ - 4 k^X = 4 i^ + j^ + k^Y = 2 i^ + 3 k^ Z = 3 i^ +  j^…

Q: Prove the property of the cross product u ∙ (v × w) = (u × v) ∙ w

A: Let the vectors , v, and w isu=u1,u2,u3, v=v1,v2,v3 and w=w1,w2,w3

Q: a. Without doing any calculation, explain why one might conjecture that two vectors of the form (a,…

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Q: 19 - By using the definition of the dot product, which vector is orthogonal (perpendicular) to å =…

A: Dot product of two vectors

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Q: Compute the cosine of the angle between the plane through P = (6,0,0), Q = (0,7,0), and R = (0,0,5)…

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Q: A fire ant, searching for hot sauce in a picnic area, goes through three displacements along level…

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Q: If u is a unit vector find the dot product of vectors u and w

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Q: Find the area of the parallelogram that has the vectors as adjacent sides.u = i − j + k, v = i + k

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Q: The position vectors of A and B with respect to the origin O are a and b respectively. M is the…

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Q: Show that the points whose position vectors 2i+ 3j – 5k , 3i +j – 2k and 6ỉ – 5j + 7k are collinear?

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Q: Express the vector H %3D p?za, + зфzaф - рф*а, at B(3, -4, 1), in CCS.

A: The given vector is H→=ρ2z aρ+ 3Φz aΦ - ρΦ2 aZ.We have to express it in the cartesian co-ordinate…

Q: Let W be the union of the second and fourth quadrants in the xy-plane. That is, let W= Complete…

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Q: compute the dot products i ⋅ j, i ⋅ k, and j ⋅ k for the unit coordinate vectors. What do you…

A: Given: Compute the dot products i ⋅ j, i ⋅ k, and j ⋅ k for the unit coordinate vectors.

Q: Which option is equal to the DOT product uV of vectors 3 u = 1 4 -4 26 24 N N

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Q: Let u and v be vectors. If their dot product is zero what is the angle between u and v (in degrees)?

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Q: Use your knowledge of vector dot product to explain why the following product is either true or…

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Q: Use a dot product to determine whether the vectors u = ⟨1, 2, 3⟩ and v = ⟨4, 1, -2⟩ are orthogonal.

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Q: Find the acute angle between the two vectors A = 2a, +a, + 3a, and B = ax – 3ay + 2a, by using the…

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Q: Find the horizontal and vertical components of the vector u that has magnitude |u|=4 and direction…

A: Given that, the magnitude is |u|=4 and the direction angle is α=20∘