42. Show that the unit vector ī = xỉ + yj is not parallel to ū = yi – xj for any choice of x and y.

Q: Let x be an n-vector. (a) Is it possible for x · x to be negative? Explain. (b) If x · x = 0, what…

A: We shall define, x→=(x1,x2,...,xn) The dot product of two vectors x→ and y→ is given as,…

Q: Q1/ If f(x,y)=find a unit vector u for which Duf (2,3) = 0 x+y

A: We have to find a unit vector u for which Duf(2,3)=0 where f(x,y)=yx+y

Q: Use vectors to show that the distance from P1(x1, y1) to the line ax + by = c is d = |ax1 + by1 -…

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Q: Suppose U and W are vectors in R" then ||U +W|| - ||U|| + || W|| if the angle between U&W is equal…

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Q: Let vector v = 3i – 2j+ 4k and point P = (0,0, -3). For what point Q is it true that v = PQ?

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Q: Consider two vectors A and B prove that the cross product between them can be calculated as follows…

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Q: 16 Jlg wo vectors ñ and m are said to be orthogonal if ħxñ=0 ulgo O ihs o

A: Two non-zero vectors are said to be orthogonal when (if and only if) their dot product is zero.

Q: · Let 2 be the separation vector from a fixed point (x', y', z') to the point (x, y, z), and let z…

A: Since r is the separation vector from the point x',y',z' to the point x,y,z and the difference…

Q: Consider two vectors A and B prove that the cross product between them can be calculated as follows…

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Q: In general, show that the vectors V = ai + bj and W = -bi +aj are always perpen-dicular. Assume a…

A: Given vectors are v=ai+bj and w=-bi+aj, where a≠0 ,b≠0. We know that two vectors are perpendicular…

Q: Let y = and u = Let L be the line spanned by u. Write y as the sum of two orthogonal vectors, YL in…

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Q: 11. Use vectors to show that the distance from P:(x1, yı) to the line ax + by = c is |ax, + by, – c|…

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Q: 13. Show that the pair of vectors i + i and i – i is perpendicular.

A: Two vectors is said to be perpendicular if their scalar product is zero.

Q: Q2/ Show that the vector v = ai + bj is perpendicular to the line ах + by + с.

A: A line and the vector  are said to be perpendicular to each other when the product of their sloped…

Q: Suppose that u and v are vectors in R7 both of length 2√2 and that the length of u - v is also²√².…

A: Solution :

Q: A vector A-xyzi+3x'yj+ (xz-y'z) k.

A:

Q: Determine the shortest distance from the point (3, 4, 5) to the line through the origin parallel to…

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Q: 3. Consider the vectors X and Y in R³ where X = -i+3j and Y = 4i - 2j + 2k. 1 Find the unit vector…

A: Given, X = -i + 3j  and Y = 4i -2j + 2k

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…

A: I have written equation of line in parametric form and then checked the direction ratio

Q: 2) If A =,find grad(div A), where r is a position vector.

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Q: Find a vector B such that F = V × B and V · B = 0, where F %3D (x + Зу, у — 2z, х - 2z).

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Q: Solve for the projection of the vector P = (3,4, 4) onto Q = (0, –2, –5). What is the exact measure…

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Q: 3. The work Wdone by = xf + 3xyj - (x + z)k to move a particle from point 1 to point 2 is defined by…

A: “Since you have asked multiple questions, we will solve the first question for you. If you want any…

Q: 1. The two unit vectors parallel to the line y = x- 3 are and

A: We’ll answer the first question since the exact one wasn’t specified. Please submit a new question…

Q: What three points are on the line L: vector r= (2,-5) + s(2,1), sER

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Q: 7 Consider the vectors: U = 1 v = w = -2 2 Express W as a linear combination au + bv. What is b'?

A: WRITE  W AS A LINEAR COMBINATION OF U AND V ie. w = au + bv Using Row Elementary Transformation,

Q: The vector y which is collinear with the vector u= and satisfies the condition u.v= 3, is O O O…

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Q: Show that the vector v = ai + bj is perpendicular to the line

A: GivenVector V = ai + bj and the line ax + by + c

Q: Q2/ Show that the vector v = ai + bj is perpendicular to the line ax + by + c.

A: Condition for perpendicular is: m1m2=-1 Part A: Consider the vector v=ai+bj x component of vector =…

Q: If u is a fixed unit vector and Duf (x, y) = 0 for all points (x, y), then f is a constant function.…

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Q: Let u¯¯¯=⟨−3,−5⟩, v¯¯¯=⟨2,−2⟩, and w¯¯¯¯=⟨2,4⟩. Find the vector x¯¯¯ that satisfies 9u−v+x=2x+w

A: Given that: u=-3, -5v=2, -2w=2, 4

Q: Find a vector perpendicular to the 2-space line: Qx - Ny + R = 0

A: Please see the below picture for detailed solution.

Q: e vector x²y?

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Q: If v = 2i + 4j and w = -2i + 6j, find the vector projection of v onto w.

A: Given vectors are: v = 2i + 4j w = -2i + 6j The formula for the vector projection of v onto w is…

Q: If ï = (, 2), find a vector i that is perpendicular to ū.

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Q: Suppose that u, v are vectors in R³, u · v = 1, || = 1, the angle between u and v is T/3, and u is…

A: According to the problem, we have

Q: 1. Plot the following vectors using arrows on an xy-graph: -- (}). v-[+]. 1 u = V = 2u, u+v. Is…

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Q: ir kümelerinden kaç tanesi R' için bir tabandır? how many of the given vector

A: A subest S of R2 is a subspace if and only if it contains the null vector whenever it contains two…

Q: Find basis for the set of vectors in R2 on the line y= nx . where n=9.

A: Explanation of the solution is given below...

Q: 2. Give the components for the velocity vector of a boat that is moving 50 km/hr toward the…

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Q: 10. Let the vector v = 2i -3j + k, and the vector w = = -i+3j+ 2k. Find v x w.

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Q: Find the length and direction (when defined) of u x v. u = -,i + +k U = i + j + 2k ||uxo ||= 8 | ||u…

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Q: 13. Describe the vector that translates LMN to L'M'N’. 6. L' L 2 N' M -6 -4 -2 4 6 N2 M -4 -6 4,

A: Translation vector

Q: State the condition that the two vectors i and y are perpendicular. Find the value(s) of k such that…

A: If two vectors are perpendicular to each other, then their dot product is equal to zero.

Q: Q1/A/ Show that in plane the non zero vector N = ai+ bj is:- perpendicular to the line ax +by +c =0…

A: We have to show that the vector N=ai+bj is perpendicular to the line ax+by+c=0. We have to find the…

Q: 12. Suppose that ú = (a, b) is a non-zero vector in R², where a ± 0. Show that the line L =…

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Q: What is the dependence on the following vectors: u=(3.0.1), v=(1,-1,0) and w=(1.0.1) thanks!

A: A set of vectors {v1,v2,...,vn} in Rn is said to be linearlyindependent if the vector equationx1v1 +…

Q: b) Show that the vector w = u – proj,u is orthogonal to proj, u

A: The expression for the vector projection of u onto v is: projvu=v·uv2v Given: u=3,4,0 and v=-2,3,-6…

Q: For what values of y are the vectors yi – 2j + 3y k and 6i +j+ 3y k orthogonal.

A: To find the values of y for which the vectors yi-2j+3y k and 6i+j+3y k are orthogonal.