Find a unit vector normal to the plane containing u =i- 3j -k and v = - 3i - j+ k. ..... A unit vector normal to the plane containing u and v is ai + bj + ck where a = and c= (Simplify your answers, including any radicals. Use integers or fractions for

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

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Q: Find the angle mesure between the two vectors u and v where : u=-2i + 2j + 4k, v=3i + 8j + 2k write…

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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: snip

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Q: Write a vector of magnitude 5, parallel to the plane 3x + 4y + 5z = 10 and perpendicular to the…

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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 the two unit vectors that are orthogonal to i = (1,2). Which two unit vectors are parallel…

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

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Q: Find the unit vector having the same direction as v. v = 3i + - 4j O A. u= 15i + - 20j OB. u- - 5 B.…

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Q: A vector of 2 unit length parallel to vector 2i + 2j+k is:

A: We know a vector consists of magnitude and direction as we have to find the direction parallel to…

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

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Q: is The unit vector in the direction of v=(4,0,–3)

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Q: Let a = 2i – j - 3k and b = 3i – j-k %3D (a) C ) Find two unit vectors orthogonal to both a – i and…

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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: Find the vector that makes equal acute angles with the positive coordinate axes and has length 2. O…

A: An acute angle is an angle that measure is less than a right angle (90 degrees). The magnitude of a…

Q: Find a unit vector in the direction of the given vector. Verify that the result has a magnitude of…

A: See below

Q: Determine a unit vector perpendicular to the plane a =21-6j –3k and b=4i+3j – *

A: Since you have asked multiple questions in a single request, we would be answering only the first…

Q: products

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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: Consider the vectors u = (2,0) and v = (-4,4). Sketch the vectors, find the angle between the…

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Q: Find the median AD of the triangle ABC where positive vectors of the vertices A, B and C are…

A: Vertices of the Triangle ABC given A=i+j,B=4i+6j,C=i-j; Hence, We can take these vectors as the…

Q: Find a unit vector normal to the plane containing u= 2i +j-k and v = -i+3j+ 2k. A unit vector normal…

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Q: Find the unit vector in the directions of v, where Ans = %3D

A: To find unit vector in the direction of v, divide it by the length of v.

Q: Find the angle between the vector through the origin & the point (1,1,1) and the component of Ā = 2i…

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Q: What is a vector that is normal to the plane 4x+6(y-100)+7(z-200)=20? O A. 4i+6j-20 k O B. 8i+ 12 j…

A: Given query is to find the normal vector.

Q: Determine a unit vector perpendicular to both A=i+2j-3k and B=-2i-3j+k

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Q: Consider the vector v = (2, y) in R?. If you rotate the vector by 90-degrees counter-clockwise, then…

A: Given,   v=2,y   in ℝ2.

Q: Find a vector normal n to the plane with the equation 5(x – 1) – 9(y – 8) + 9z = 0. (Use symbolic…

A: Given, Equation of plane is given as: 5x - 5 - 9y + 72 + 9z = 0 5x - 9y + 9z + 67 = 0   For a vector…

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

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Q: i +j +k andi – j -k.

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

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

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Q: If a = 2i+j-k, b=-i+2k, and c=i+2j-2k, (i) Find a unit vector perpendicular to the plane of a and b.…

A: Let two vectors be defined as x=x1i+x2j+x3k and y=y1i+y2j+y3k . The dot product of the vectors, x ,…

Q: Find two unit vectors that are perpendicular to both j + 2k and i – 2j + 3k.

A: Given that a→=j+2k,  b→=i-2j+3k   We know that the cross product of two vector is perpendicular to…

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

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Q: Find the normal unit vector perpendicular on à and B for A = 2i+3j-k and B=-j+2k %3D

A: To find the normal unit vector perpendicular to A and B

Q: Find a vector w that bisects the smaller of the two angles formed by 15 i + 8 j and 40 i – 9 j. w =

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Q: Find a unit vector normal to the plane containing u=i+ 3j - 2k and v = -i- 2j + 3k. A unit vector…

A: To find the unit vector normal to the given vectors

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: Find a vector v parallel to u=−7i+j−6k and with magnitude ||v||=12.

A: Given,          A vector v parallel to u=−7i+j−6k and with magnitude v=12.

Q: 2. Find an unit vector perpendicular on both a =i +2]- and 6 2i -k.

A: According to our guidelines, In case of multiple questions we are supposed to answer the first…

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 the angle between the vectors i + j + 2k and 2i - j +k

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Q: Determine two unit vectors, vand wl, perpendicular to the plane passing through the z-axis and point…

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Q: Find unit vectors Parallel to the YZ Plaane and PerPendicular to the Vector V = 51-j+2k ?

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Q: Find two unit vectors that are perpendicular to both j + 5k and i − 4j + 3k. (Enter your…

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Q: Find the unit vector u in the direction of v. Verify that u| =1. 12. (1,–6)

A: solution is given below..

Q: Find a unit vector that is orthogonal to both u and v.       u = −3i + 2j − 5k,    v = i − j + 4k

A: u=-3i+2j-5k,  v=i-j+4k Now the vector orthogonal to both u and v is, w=u×v=…

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: 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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