For the vectors A=x + 2ŷ – î = (1, 2, – 1), B=ŷ + î = (0, 1, 1), C=î-ŷ = (0, 1, 1), a) Prove that Ax (B x C) = B (A · C) – C (A · B) b) Find unit vector in the direction of A vector

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: Find a unit vector normal to the plane containing v=2i+3j-k and . w = -2i - 4j - 3k.

A: Given: v=2i+3j-k  w = -2i - 4j - 3k.

Q: Find a vector, AB , with magnitude 4 in the direction of PQ where P and Q have coordinate (5,0, 8)…

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Q: (A) Find the vector that is Normal to: A = 2i + 3j +k and such that it is lies in the plane…

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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: Verify the Pythagorean Theorem for the vectors u and v.u = (1, −1), v = (1, 1)

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Q: Find a unit vector u in the direction of the vector from P1(1, 0, 1) to P2(3, 2, 0).

A: Concept: Unit vector is a quantity which has a magnitude as 1and as well as direction, it is also…

Q: Verify that the two planes are parallel. -x + 6y + 2z = 8 -x + 3y + z = 9 2. Find the normal vector,…

A: Find your answer below

Q: Find c so that the vector v is orthogonal to W = ||

A: Given: v=1c. w=2-1 Vector v and w are orthogonal only if the dot product of vectors is zero.

Q: Find the angle between the vectors u = (1, −1) and v = (0, 1).

A: Given query is to find the angle between the vectors.

Q: Find two unit vectors that are parallel to the yz-plane and are orthogonal to the vector 10i – 2j +…

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Q: Find r so that the vector from the point A(1,−1, 3) to the point B(3, 0, 5) is orthogonal to the…

A: The vector from the point A(1, -1, 3) to the point B(3, 0, 5)            Is orthogonal to the vector…

Q: find the given vector  Vector of length 2 in the direction opposite to v = i − j

A: A vector oppositely directed to v=i-j is is u=-v=-i-j=-i+j                   u=-i+j A unit vector eu…

Q: Find the vector v of length 6 that has the same direction as the unit vector (1/2, V3/2).

A: Consider the following values: magnitude=6unit vector=12i^+32j^

Q: Find the x-component of the vector of length 3 in the direction of V = (-1,-1).

A: v=<-1,-1>=-i-j Unit vector in the direction of vector V i.e.,     v⏜=-i-j(-1)2+(-1)2 =-i-j2…

Q: Find the vector z, given that u = , v = , and w = . z = 8u - 3V - -W 2 1. Z =

A: We have been given the vectors  u = <1, 2, 3> v = <2, 2, -1> w = <4, 0, -4>

Q: products

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Q: Find the values of x such that the angle between the vectors u = (2, 1, -1) and v = (1, x, 0) is…

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Q: Decompose v into two vectors v, and v2, where v, is parallel to w and v, is orthogonal to w. v = 2i…

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Q: M contains the point with coordinates (0,0,1) 2 M is orthogonal to the vector 0

A: Introduction: The general equation of Plane is ax-x1+by-y1+cz-z1=0

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

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Q: Find the unit vector in the direction of v = (3, −1, 2), and verify that this vector has length 1.

A: Vector v = (3, −1, 2) Such that,

Q: Find a vector function that represents the plane that passes through thepoint p0 with position…

A: The plane passes through the point p0 whose position vector is r0→. The plane also passes through…

Q: Find a unit vector orthogonal to A in the plane of B and C if A = 2i - j + k, B = i + 2j + k, and C…

A: The given details are as follows.

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: Find a unit vector that is orthogonal to both i+j and i+k ?

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

A: Follow the procedure given below.

Q: Find a unit vector orthogonal to the vector A= 2i-j+k and parallel to the vectors B= 2i+2j and C=…

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Q: The vectors a and bare unit vectors such that a a+b and 2a +jb are perpendicular. --Determine the…

A: The given vectors a→ and b→ are unit vectors such that a→.b→=12.Given: a→+b→ and 2a→+jb→ are…

Q: The vector w is a unit vector, and the vector i is any non-zero vector. If z = (x · W)w and ỹ = i –…

A: Use the property of dot product and associative and distribute property to solve the problem.

Q: Decompose v into two vectors Vị and v2, where vi is parallel to w and v2 is orthogonal to w. v - -2i…

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Q: Find a unit vector perpendicular to i-j and to i +k and with a positive k component.

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Q: Let vectors u=[1,0,-1] and v=[-2,1,2].Find the vector w that is orthogonal to both u and v

A: The given vector is u=[1,0,-1] and v=[-2,1,2]

Q: Find the vector projection of vector u onto vector v, and find the vector component of u orthogonal…

A: The projection of vector u onto v is given by projvu=u⇀v⇀v⇀2v⇀

Q: For any vectors U, V and scalars a, b, prove that (aU) x (6V) = ab(U × V) (a) (b) (aU) - (bV) = ab(U…

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Q: Show that the vectors (x1, Y1) and (x, 2) in V, (F) are linearly dependent if

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Q: Find a unit vector orthogonal to both u and v. u = -3i - 2j - 5k li 1 3i+ -j + 4 10 V = - 2

A: To find A unit vector orthogonal to both u and v

Q: Find a vector, in component form, that is orthogonal to the plane containing the points P = ( – 1,…

A: find the explanation below

Q: 2 -a) Find a unit vector perpendicular to the plane that passes through the points P(1,4, 6), Q =…

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Q: Find a unit vector that is orthogonal to both i +j and i + k.

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Q: Find the values of ( x ) such that the vectors and are orthogonal.

A: Given: The two vectors are: 3,2,x and 2x,4,x Also, the two vectors are orthogonal.

Q: Using the vectors from the previous problem, find the projection ul of v onto the vector u and find…

A: We say that 2 vectors are orthogonal if they are perpendicular to each other. i.e. the dot product…

Q: Let v be the vector from initial point P1 = (4, -5) to terminal point P2 = (4, 3). Write v in terms…

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Q: b/Let u and v be a nonzero vectors in 3- space, and let e be the angle between these vectors when…

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Q: |A force F = 9i + 8j – 4k is applied to a spacecraft with velocity vector v = 2i – 7j. Express F as…

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Q: perpendicular to the plane formed by the vectors w1 = [1 2 1] and w2 = [2 2 3], with the z axis

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Q: Decompose v into two vectors, v, and v2, where v, is parallel to w and v, is orthogonal to w. v =…

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