Find a unit vector normal to the plane containing u= 2i +j-k and v = -i+3j+ 2k. A unit vector normal to the plane containing u and v is ai + bj + ck where a = b: , and c = (Simplify your answers, including any radicals. Use integers or fractions

Q: Let V be the set of vectors shown below. V= x> 0, y>0 a. If u and v are in V, is u +v in V? Why? b.…

A: Please check step 2 for solution.

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

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Q: If a = i+ 3j +k and b = i+ 9j +k, find a unit vector with positive first coordinate orthogonal to…

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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: 3. Use the dot product to determine whether the vectors are parallel, orthogonal, or neither. v = 4i…

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Q: Find the angle between the vectors. (First: v = -21 exact u = i- 6j + k, approximate xx x +

A: topic:- vector algebra

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

Q: If a = i+ 2j +k and b = i+10j + k, find a unit vector with positive first coordinate orthogonal to…

A: The vectors are given as , a→=i^+2j^+k^ and b→=i^+10j^+k^ find a unit vector with positive first…

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

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A: Given that the plane Π2 contains the point O, A and B and the plane Π3 contains the points O, A and…

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Q: Find the angle between the two vectors A = i +j+k and B = 2i+j-k

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Q: The unit vector perpendicular to the vectors n1= i-j+3k ,n2=2i+j+3k is a vector?

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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,…

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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…

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Q: If a = i+ 2j + k and b = i+ 5j +k, find a unit vector with positive first coordinate orthogonal to…

A: Given that     a = i+2j+k and b = i+5j+k We have to find a unit vector with positive first…

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.

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Q: If a = i+5j + k and b = i+ 9j +k, find a unit vector with positive first coordinate orthogonal to…

A: We have to find

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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…

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A: Vector cross product of given two vector  is orthogonal to two given vector

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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: If r is equal to 300 mm, Find: 1.) Rectangular form of r in ft 2.) Unit vector of r

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Q: Express the following vectors in Cartesian (component) form. a) f has magnitude 20 and direction…

A: Solution:-

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

A: This question is based on finding curl of two vector.

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

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Q: (b) Find a vector i that is parallel to ↑ and perpendicular to L.

A: As per your demand, we solve part b) only

Q: Find a unit vector in the plane of the vectors A = i + 2j and B = j + 2k, perpendicular to the…

A: Consider the given question,

Q: find the two-dimensional vector equation of the line r(t) = a +t*m such that - r(0) has norm 8 and…

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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 unit vector orthogonal to both u and v.u = 3i + j v = j + k

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

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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: If a = i+ 3j + k and b = i+9j + k, find a unit vector with positive first coordinate orthogonal to…

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

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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: Þ(x, y, z) = e¬x²-y²-z²+2yz

A: First take gradient and magnitude of gradient