A vector is A=3i+7j and B vector is B=2i-5j+2k. C vector is C=A+B where ij,k are the unit vectors of x,y,z directions respectively. Find the magnitude of the vector product C*C.

Q: When analyzing the vector To the sum of two vectors, the first is parallel to the vectorA 2i-j+ 3k…

A: I am attaching image so that you understand each and every step.

Q: Find the angle (in radians) between the 2 vectors U(-3, 4, -4) and V(1, 2, 2)

A: Given vectors are,               U(-3, 4,-4 ) and V(1, 2, 2 )

Q: For the vector u = 4i- 3j, find a unit vector a. in the same direction as u b. in the opposite…

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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: We can solve this as follows:

Q: Determine a unit vector perpendicular to the both vectors A : 2i + 5j – 4k and B - 3i + 6k. |0| = (…

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Q: 3. Find the angles between the vectors: u = 2i + j, u = 2i – 2j + k, v = 3i + 4k a. v = i + 2j – k…

A: a.)u=2i+j , v=i+2j-klet θ be the angle between the…

Q: 3. Find the angles between the vectors: u = 2i + j, v = i + 2j – k b. u = 2i – 2j + k, v= 3i + 4k а.…

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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: 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: Find a vector v parallel to u=4i−3k and with magnitude ||v||=4

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Q: Find the angle 0 between vectors u = 2i - jand v = 6i + 4j.

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Q: Let the vector 3i +j can be expressed as a sum of vectors u and v where u is parallel to the vector…

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Q: Find a unit vector (a) in the direction of v and (b) in the direction opposite of  v = ⟨2, −1, 2⟩

A: a) Given that v=2, -1, 2 So unit vector in the direction of v is  vv=2, -1, 2(2)2+(-1)2+(2)2=2, -1,…

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: 18 Find the Unit Vector that has the Same direction as vector V = 8i-6j

A: Given :  V = 8i - 6j

Q: Construct the vectors a = 3k - 2j and b = 3i - 2j and c = ax b. Compute the absolute value of the…

A: Given data : a⇀=3k-2jb⇀=3i-2j To calculate c=a×b The value a×b=ijk0-233-20

Q: Use the dot product to find the angle between the vectors v =i – 2j + k and w = i+j-2k. For which…

A: First we have to find the angle between the vectors v and w where v=i-2j+k and w=i+j-2k. For this,…

Q: When decomposing the vector into the sum of two vectors the first is parallel to the other vector…

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Q: Find the unit vector u in the directionof the vector v=(1, 2, -2). 8.

A: Given,           v=1,2,-2

Q: The plane contains the point (−2, 3, −1) and is normal to the vector 3i − 2j.

A: Given: point -2,3,-1   and vector 3i-2j

Q: products

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Q: 2.) Find two vectors that are orthogonal to the vector v = 8i - j

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Q: A. Give the Cross products of the unit vectors (i, j, k).

A: Understanding of cross product of three vectors are required to under this.

Q: Find a unit vector perpendicular to the plane of P(1, -1, 0), Q(2, 1, -1), and R(-1, 1, 2) .

A: Given P(1, -1, 0), Q(2, 1, -1), and R(-1, 1, 2) .

Q: The vector from the origin to point A is given as (-2, -4, 5) and the unit vector directed from the…

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Q: 15. Given the vector u (2i + 5j) and vector v = (3i + 4j), find the dot product u v %3D

A: We have to find the dot product of given vectors.

Q: find the component form of the vector. The vector 2 units long in the direction 4i - j

A: Given vector is u = 4i – j. So, the unit vector in the direction of the given vector is

Q: Find the projection of the vector v onto the vector w if v = 2i + j and w = 6i + 3j

A: we have given v and w vectors . We have to find the projection of the vector v onto the vector w

Q: ': Find all unit vectors parallel to the and perpendicular to the plane vector V = 5i -j + 2k

A: Here we find all unit vector parallel to the yz plane and perpendicular to the vectorv→=5i∧-j∧+2k∧

Q: Find the angle between the vectors u (2, –1) and v = (1, 1).

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Q: Use vectors =(-1, 1), v= (7, –2), and w= (0, 4) to find (u w)v, and determine whether the result is…

A: We can answer it as below

Q: Find all unit vectors parallel to the JZ plane and perpendicular to the vector V = 5i -j + 2K %3D

A: A vector is parallel to yz-plane and perpendicular to the vector v, we have to find the unit…

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

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Q: The vector i +bj-k is perpendicular to the vector I +2j-3k. what is the value of b?.

A: We know that if two vectors are perpendicular to each other then there dot product is zero. Given,…

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

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Q: Find a unit Vector orthogonal to both vectors: U =21 +5j-K and V=i+3j-2K.

A: We can find the unit vector as below

Q: Find the unit vector u in the direction of the vector v=4(2, 1, 2).

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Q: Find the two unit vectors orthogonal to both a = 3j + 2k and b = -i- 2k. O A -61 - 2j + 3k and 6i+…

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

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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: compute the dot products i ⋅ j, i ⋅ k, and j ⋅ k for the unit coordinate vectors. What do you…

A: Given: Compute the dot products i ⋅ j, i ⋅ k, and j ⋅ k for the unit coordinate vectors.

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: 8 Find the 3-dimensional unit vector in the direction: a 2i + 3k 6 -i+ 2j – k c 2i – 2j + k

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Q: Find a unit vector that is perpendicular to both u = (1,0, 3) and v = (-1,2,0). Answer:

A: We have to find the unit vector which is perpendicular to given vectors.

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 following for the vectors u = 6i + 9j + v2k and v = - 6i – 9j – V2 k. a. v•u, v, and u b.…

A: We have to solve

Q: Find a unit vector u in the direction opposite of v = (2,8,-3).

A: Solution ) v =  { 2 , 8 , -3 }   vector with same magnitude and opposite direction   = { -2 , -8 , 3…

Q: Find a unit vector u in the direction of the given vector. (- 1,2)

A: The given vector is, < -1, 2 >.

Q: R) Find the area of a triangle formmed from the two - = c'+2j=k-- - 2i-jtuk. Vectors-a- 6 = 2i-j+4k,

A: Given: a=i^+2j^−k^b=2i^−j^+4k^