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

Q: Find a unit vector that is orthogonal to both u = i − 4j + k and v = 2i + 3j.

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Q: Find a unit vector that is orthogonal to both u and v for u = and v = .

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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: Decompose v into two vectors, v1 and V2, where v is parallel to w and v2 is orthogonal to w. v=i+j,…

A: A vector parallel to w can be obtained from the following formula, v1=v.ww2w and the other vector…

Q: Determine the constant a so that the vector i = (2x + 3y)î + (2y – 2z)j+ (x + 2az)k is a solenoidal.

A: Given : The vector v→ = (2x + 3y) i^ + (2y - 2z) j^ + (x + 2az) k^.   To determine the constant a so…

Q: s opposite direction to the vector u = .

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Q: Find the angle 0 between the vectors. (f. 9) = L R f(x) = 3x³, g(x) = 4x4, %3D f(x)g(x) dx radians

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Q: Evaluate /| F - d5 , where F = and S is the helicoid with vector equation r(u, v) 0 < u < 4, 0 < v…

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Q: Evaluate, don't forget the constant vector, (ri - 2tj + k) dt

A: We have to evaluate the integral: ∫t2i-2tj+1tkdt We know the formula of integration,…

Q: Evaluate |/ V1+ x² + y°dS, where S is the helicoid with vector equation r(u, v) = 0 < u < 4, 0 < v…

A: Given surface integral is  ∫∫S1+x2+y2 dS where S is the helicoid with vector equation  r(u,v) =&lt;…

Q: Find the coordinates of the point P on the line and a vector v parallel to the line. X = 4t, y = 4 –…

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Q: Q4) The vector product of two vectors is scalar product. F O T

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Q: Find the positive value for which the vector r(t) = (3t, 10t², 7t² – 2) is perpendicular to r'(t).

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Q: Find the coordinates of a point P on the line and a vector v parallel to the line. X - 8 y + 2 = z +…

A: This question is based on 3-d coordinate geometry.

Q: Find the vector projy u. v = i+ j+ k, u = 4 i + 12 j+ 3 k 10

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Q: Write the vector x=0 as a linear combination of the vectors u=0, v= 1, w= 1 1

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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: Write the vector as a linear combination of the unit vectors i and j.

A: Given two unit vectors i and j.  To write the linear combination of i and j.

Q: Find a non-zero vector & perpendicular to the vectors v = x = ► 3 H and u = 4

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Q: Find the cross product of the unit vectors. jx i

A: Topic :- Vector

Q: For any vector v in ℝ3, explain why v × v = 0.

A: Given v∈R3 v×v=0

Q: Find the coordinates of the point P on the line and a vector v parallel to the line. x = 8t, y = 8 –…

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Q: Determine a unit vector in the direction in whichf(x,y) = 4x³ y² increases most rapidly at point…

A: Given that : - f(x,y)=4x3y2    at  P(-1,1) A function f(x,y) increases most rapidly at pointy P(a,b)…

Q: H.W 8- Find a vector in the opposite direction of a = (4,10) but as long. 4

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Q: Find the value of c that will make the vector 2 lie in the span of 0 2 and

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Q: Find the coordinate vector of w relative to the basis S = {u1, u2} for R2. : (6, – 6), u2 = (2, 2);…

A: Here we have to find the coordinate vector of w relative to the basis S ={u1,u2} for R2 . Here…

Q: Find a vector w perpendicular to both vectors u=2i-j+2k and v=3j-4k w=i+2j-3k w=-2i+8j+6k…

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Q: e vector x²y?

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Q: Find the angle 0 between the two vectors u = and v = .

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Q: Find the magnitude of vector v. Y -2 w X

A: We have to find the magnitude of v

Q: Evaluate /1+ x² + y°dS, where S is the helicoid with vector equation S r(u, v) 0 < u < 3, 0 < v <…

A: Given integral ∬S1+x2+y2dS, where S is helicoid with vector equation r^u,v=ucosv,usinv,v We have to…

Q: Evaluate /| F. d5 , where F = and S is the helicoid with - vector equation r(u, v) = 0 < u < 1, 0…

A: To evaluate the below vector surface integral. ∫∫SF⋅dS

Q: Determine the i - component of the cross- product for the two vectors: x = ai+bj+ck and y = di+ej+fk…

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Q: Find the coordinates of a point P on the line and a vector v parallel to the line. x - 8 y + 3 = z +…

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Q: Show that the vectors v1, V2, and v3 are linearly dependent, where n- . -. 3 V2 = 5 and v3 = 6 Vi =…

A: The given vectors are v1=12, v2=34 and v3=56

Q: (:) R de u = ve v = ( t2 ) for vectors, show = 2u1v1 + 3u2v2 is an internal product

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Q: Evaluate / V1+ x² + y°dS, where S is the helicoid with vector r(u, v) 0 <u < 3, 0 < v< T

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Q: What is the magnitude of a vector joining two points P(x1, y1, z1) and Q(x2, y2, z2)?

A: The two points  are : P(x1, y1, z1) and Q(x2, y2, z2). As the vector is directed from point P to Q ,…

Q: Find the component of V, |V|= V5 in the direction of a vector from A(0,0, 4) to B(2,5, 0).

A: The vector joining the points A0,0,4 to B2,5,0 is given by, AB→=2-0i^+5-0j^+0-4k^=2i^+5j^-4k^ The…

Q: Evaluate 1+ x2 + y?dS, where S is the nelicoid with vector equation (u, v) 0 < u< 2, 0

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Q: Evaluate 1+ x² + y*dS, where S is the helicoid with vector equation r(u, v) 0 < u < 2, 0 < v < 2T

A: Given ∬S1+x2+y2dS where S is the helicoid with ru,v=u cos v, usin v, v, 0≤u≤2, 0≤v≤2π. Since ru,v=u…

Q: H.W 9- Given that a = (1,1) and b = (-1,0). Find a vector in the same direction as but a+b %3D %3D…

A: Given: a→=1,1, b→=-1,0 To find: A vector in the same direction as but a→+b→ five times as long.

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

A: The given vectors are: u=314 and v=22-4 Multiply the numbers component wise to find the dot product…

Q: Find self-value and self-vectors.

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Q: Find a vector 2 units long in the direction of v = 4i - j + 4k.

A: First find a unit vector in the direction of v = 4i - j + 4k.

Q: Find the addition of the vector using the component methods. 1. 9 m/s [N30°E] and 2 m/s [N 60°E].

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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: Evaluate /1+ x² + y²dS, where S is the helicoid with vector equation т(и, 0) - = 0 < u < 3, 0 < v <…

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Q: Þ(x, y, z) = e¬x²-y²-z²+2yz

A: First take gradient and magnitude of gradient