If F(x,y,z)=1i+2j+3k, then O1. P=1 Q=2 and R=3 are vectors of F. O II, P=1 Q=2 and R=3 are gradient vectors of F. O II, P=1 Q=2 and R=3 are scalars of F. OV. P=1 Q=2 and R=3 are vectors fields of F.

Q: (3) Suppose a vector x is orthogonal to vectors u and v. Show that x is orthogonal to u+v.

A: We will use the fact that x is orthogonal to u and v to prove that x is orthogonal to u+v also

Q: If L is a line in 2-space or 3-space that passes through the points A and B, then the distance from…

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Q: 1. y -2+ 2.

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Q: Question 6 Let A' = [-4 16 8] and B' = [-1 x² 21 For which real value(s) of x are vectors A and B…

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Q: Prove that the vectors (1,1,0), (3,1,3) and (5,3,3) are linearly dependent.

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Q: Calculate r'(t) and T(t) and evaluate T(1). r(t) = (6 + 7t,12,5 – 1²) (Give your answers using…

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Q: 1. Consider the pointsS= (1,−3) andT= (2,5).(a) Sketch the vector−→ST.(b) Give the component form…

A: Here 2 different problems are provided. As per our Bartleby Guidelines, we are supposed to…

Q: 1. Find the vector component of the vector ū (-3, 6, 2). [28, 63, 0] in the direction of = %3D

A: We have to find vector component of u =[28, 63,0]  along the direction v=[-3, 6,2] Vector component…

Q: If A and B are both second-order tensors and t, u, v, and w are all vectors, prove the following…

A: Given that if A and B are both second-order tensors and t, u, v, and w are all vectors.   (1). To…

Q: Find a vector orthogonal to both v and u. V = 2i - 2j + k, u = -4i - 4j + 5k -6i - 7j + 7k 6i + 7j +…

A: Given is           v = 2i -2j +k           u = -4i-4j +5k         two vector a & b said to be…

Q: Let ū = (4, –2), ū = (-2,0), and w = (2, 2). Find the vector x that satisfies Tu – u +x = 5x + w. In…

A: Given Let Plugging the values in the equation:

Q: (a) Show that the vectors v = and w = 2 are linearly independent. (b) Explain why 3 vectors in R" of…

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Q: (a) Suppose A=(S,+S) and B (S-S), Show that S = A + B A= A and B =-B (b) Suppose that A B, is a…

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Q: Find a vector equation for the line through the point (4, 5, -1) perpendicular to the vectors , 6,…

A: we have to find the line equation passing through point (4,5,-1) and perpendicular to the vectors…

Q: 18 as a linear combination of a and y Express the vector v y.

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Q: Find the values of x, y and z that satisfy the vector equation 1 3 ·A·B·0-0-0-0 x 3 +y -2 +2 1 = 1…

A: We want to find values of x, y and z which satisfy given equation.

Q: Two linearly independent vectors in R3 span R2, is that true

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Q: Are the following vectors Linearly Independent? Show your work vų = [2 4 – 5], v2 = [7 2 – 1],v3 =…

A: Let x, y , z be three scalers. Condition for these vectors to be independent :

Q: 4. Prove that the vector given by (2xy -y')7+(2x²y-3xy² +2) 7 is a gradient. Also, find the function…

A: The solution are next step

Q: Use Exercise 47 to show that if cos α, cos β, and cos γ are the direction cosines of a vector v,…

A: cos2α,cos2β and cos2γ are the direction cosines of the vector v

Q: Find the coordinate vector of = 48 [B = 5 -1 with respect to the basis B = 0 {} for R³.

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Q: For the vectors à = (1, 0, −4) and ¯` = (5, 2, 1) what is the scalar a projection of onto a 1/17 √17…

A: The vectors are given by÷

Q: If L is a line in 2-space or 3-space that passes through the points A and B, then the distance from…

A: Answer is 10.1