20. 3(u · v) For Exercises 19–28, use vectors u = (-4, 1) ,v = (5, -2) , and w = (0,6) to perform the indicated operation. Then determine whether the result is a scalar or a vector.

Q: express vector as a product of its length and direction. 1/(3)^1/2 i + 1/(3)^1/2 j + 1/(3)^1/2 k

A: Let the given vector is: v=13i+13j+13k

Q: Find a unit vector orthogonal to both u = (1, -2, 1) v =(2, 1, 0)

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Q: Find the area of the parallelogram that has the given vectors as adjacent sides. Use a computer…

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Q: Write the vector equation for the line of intersection between the planes π1:x−z=−5 and π2:x−y=−1.

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Q: 4 В T(t+h) A 21 y 01 2

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Q: Explain why u + v • w _is not defined, where u, v, and w are nonzero vectors.

A: Given 3 non zero vectors : u , v and w. We need to explain why  u + v . w is not defined.

Q: How are a vector and a scalar different?

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

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Q: The plane contains the origin and is normal to the vector&lt;4, −1, 5&gt;.

A: Given: (4, −1, 5

Q: 2 3 Let u and v %3D . Find the length of 2u and the length of -v. - Find the distance between u and…

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Q: What is the i-component of unit vector of the vector u ? Give your answer correct to two decimal…

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

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Q: Howed Find efuation fer fendicular to the vector from origin to A. of the plane through…

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Q: Find a unit vector perpendicular to plane PQR determined by the points P(-3, 3, -4), Q(4, -1, - 23),…

A: Given query is to find unit vector perpendicular to PQR.

Q: Find equation of Plane that an contains the vector: and 1-6 and Z=36

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Q: Find the vector projy u. u = 3 i - j+ 3 k, V = 2 i+ j+ 2 k

A: We want to have projection vector. Projection of vector u on v is given by u.vvv⏞

Q: Define irrotational vector. Is the vector A =(6xy+z³)i+(3x² - 2)j+(3xz² – y)k irrotational? Justify…

A: we have the vector A=(6xy+z3)i+(3x2-z)j+(3xz2-y)k we have to check weather the given vector is…

Q: s the vector ở = (-1,–2,3) perpendicular to the plane 3x + 6y – 9z + 5 = 0? %3D

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Q: Evaluate F - dS, where F = and S is the helicoid with vector equation r(и, о) - = 0 < u < 2, 0 < v…

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Q: Explain why u + v ∙ w is not defined, where u, v, and w are nonzero vectors.

A: Let us assume that u,v, and w are nonzero vectors.  The dot product of the vector of the scalar…

Q: Let v =5j and let u be a vector with length 3 that starts at the origin and rotates in the xy-plane.…

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Q: For which positive value of x are the vectors (-14x, 2, 1), (2, 3.x², –10) orthogonal?

A: Given:- vectors &lt;-14x, 2,1&gt; , &lt;2, 3x2, 10&gt; To find:- positive value of x when both…

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: Describe all vectors v that are orthogonal to u

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Q: Find a unit vector u in the direction of v. Verify that u|| = 1. v = (-6, -4)

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Q: yi – aj (x2 + y?)4 Consider div (a) Is this a vector or a scalar? scalar (b) Calculate it: yi-zj div…

A: a) The divergence of a vector point function is a scalar quantity being the dot product of two…

Q: a. Please provide a well explained answer for the follwoing. And explain what are the components of…

A: Components of vector  In two dimensional ,any  vector can divide into two components x -…

Q: Calculate the coordinates of the vector w obtained by rotating anticlockwise the vector v= [0, -1,…

A: When a coordinate is being rotated along the direction of a vector by a certain angle, the new…

Q: Find a vector parametrization of the line through P = (0, –8, 7) in the direction v = (7, 0, 0)

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Q: Let u = -2i + 3j, v = 6i - j, w = -3i. Find the specified vector or scalar lu + vl2 - lu - vl2.

A: The given vectors are  u=-2i+3j , v=6i-j  ,w=-3i To find: the value of u+v2-u-v2. Solution: Since,…

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 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 non-zero vector 7 perpendicular to the vector u = 5= [8]. 6

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Q: Is it possible to take a dot and cross product of a scalar with a vector? Explain with example.

A: It is not possible to take a dot and cross product of a scalar with a vector.

Q: Describe all vectors v that are orthogonal to u

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Q: Find a unit vector u in the direction of v. Verify that llull=1 v=(15,0)

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Q: Express the vector H %3D p?za, + зфzaф - рф*а, at B(3, -4, 1), in CCS.

A: The given vector is H→=ρ2z aρ+ 3Φz aΦ - ρΦ2 aZ.We have to express it in the cartesian co-ordinate…

Q: Find a unit vector perpendicular to plane PQR. Р(1, -1, 2), Q(2, 0, — 1), R(0, 2, 1)

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

Q: REE - Sept. 2014/ Sept. 2015 / Apr. 2018 2. What is the unit vector orthogonal both to 9i + 9j and…

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Q: Find Vw. w = 6 In V10x² + y² + 4z2 NOTE: Give your answer in unit vector notation; that is, in terms…

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Q: Explain why the vector 2u × 3v points in the same direction as the vector u × v.

A: Consider the vectors: u=x1i^+x2j^+x3k^v=y1i^+y2j^+y3k^

Q: Use the vectors u= (3, 6), v=(-6,5) to find the indicated quantity. State whether the result is a…

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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: Let u = -i + j, v = 3i - 2j, and w = -5j. Find the specified scalar or vector: proju (v - w)

A: Given that, u = -i + j v = 3i - 2j w = -5j Then we get, v - w = (3i - 2j) - (-5j) = 3i - 2j + 5j =…

Q: IF: A = 2i - j+2k and B=9i+20j + 12k Find: Unit vector for A direction. Unit vector for B direction.…

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Q: Find a unit vector in the xy plane that is orthogonal 2 to 4 6

A: We have to find the unit vector.