2. Find the value of a for which the vector à = (axy – z³)î + (a – 2)x²j + (1 – a)xz²k have it's curl identically equal to zero.

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

A: A line passes through the point -6,4,1 and perpendicular to the vectors u→=-1,-2,3 and v→=3,-8,-9 We…

Q: Let I and g be unit vectors. Hence T-T= -G = 1. Calculate the inner products I (-1) and (T+g) -…

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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: Given the point D(−4, 5, 3) and A = yax + (x + z)z ay, express the D and A in: Kindly answer in…

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Q: 1. Find a unit vector perpendicular to the line passing through the points (1, 0, -3) and (2, 1,…

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Q: Let P = (4, 1, a), Q = (-2, 0, b) and v=i − 3j + 4k be two points and a vector in R³ respectively.…

A: The given points are 4,1,a and -2,0,b. The given vector is v=i-3j+4k in ℝ3.   The vector equation of…

Q: The vector fields are defined as A= aρ +2aφ +3az .  B = αaρ +2βaφ -6az both vectors are parallel…

A: Two vectors are parallel if multiplying one vector by some constant leads to another vector. A = CB…

Q: Find the equations of the traces in the coordinate planes and sketch them z = x2 +9y2

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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: If a charged particle of charge q� is travelling with a velocity v� in a magnetic field B,�,  then…

A: The objective of this question is to find the direction of the force that a moving proton feels when…

Q: . Show that (x, y) = 4x1y1 – 7x2y2 for vectors x = (x1, x2) and y = (y1 y2) in R2 defines an inner…

A: Given two vectors x and y in R2. We need to show that the given function in x and y defines an inner…

Q: Given A = x(2z -y) + ŷ(3x-2z) – 2(x+3y), find a unit vector parallel to A at point P =(-2, 1,–3).…

A: Vector valued functions are the rule that used to fix or associate a vector to a particular point…

Q: 3- The scalar component of the vector F in the direction of K is (K.F А- .K, В- K C-

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Q: Q2) Find the coordinate vector [x]B of x relative to the basis B={b1, b2}:

A: Let us consider a vector V  with the basis b1,b2,......bn then any vector v∈V is written as linear…

Q: the constant 'c' such tha 5y)âz + (y – 3x)ây z)âz

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Q: Q1. If O (0,0,0) in (x,y,z) 3-D space and r(2,5,1) draw the vector in 3D and find its direction.

A: Plot point in 3D

Q: Given ri = 3i - ej +In2 k, r2 = 5i + 7 e'j - 4 k and r3= 7i-7j+ k. Find the unit vector of (a)…

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Q: Find basis for the set of vectors in R'on the line y = nx. Where n=9.

A: Note that ℝ2 forms a vector space over the field of Real numbers ℝ. Let W =x1x2∈ℝ2  : x2 =9 x1 ,…

Q: Show that the vectors a = 3i−j+4k, b = i−3j−2k and c = 4i−3j+2k are linearly independent. Find…

A: The given vectors are  a = 3i−j+4k, b = i−3j−2k and c = 4i−3j+2k

Q: Find a unit vector parallel to the vector a´. a'= (-2,3,–1)

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Q: Let z = 2i and w=3-i. Locate the numbers 2z+w, z-3w vectorially.

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Q: Let z = 6. and y Find the vectori = 47 - 7j and its additive inverse.

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Q: or function By – k1 z) + ay (kz y + z) onal, then the values

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Q: 2 Let I be the line in R³ that consists of all scalar multiples of the vector w = -[] 2 Find the…

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Q: Prove: iv. if (x, y) = 0 for all x € R², then y must be the zero vector.

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Q: Calculate the curl of the vector = (2x + 3y)i + (y+z)j + (xy + 2zx)k

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