Let u =(0,1,2) and v=(-2,2,0). Find %3D a. A vector w orthogonal to both u and v. b. The area of the parallelogram with u and v as adjace

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: let u = [-3, 4] and v = [2, -5]. Find (a) thecomponent form of the vector and (b) its magnitude. -2u

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Q: (a) find the projection of u onto v and (b) find the vector component of u orthogonal to v.

A: (a) find the projection of u onto v and (b) find the vector component of u orthogonal to v.…

Q: Let A and B be nonzero vectors. Find k e R such that A – kB is orthogonal to A + B.

A: We know if a vector P→ is orthogonal to another vector Q→ then scalar product (dot product) is zero.…

Q: find the value of k for which the vectors u and v are orthogonal.  u = 2i - kj v = 3i + 2j

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Q: Given Ā =,B = and C =. Find: a) the scalar projection of B onto C – À b) a unit vector ū in the…

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Q: Find the component of the resultant vector. u = v = Find: u +v

A: If the vector u=a1,b1 and the vector v=a2,b2 then the resultant vector u+v is; u+v=a1+a2 , b1+b2…

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: Let h ( x , y ) = ln ⁡ ( ( x + y ) 2 ) . If you are at the point ( e , e ) what unit vector makes D…

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Q: Let L be the line y = 6 – 4x in R?. Find vectors a and b so that v = a+tb is a vector equation for…

A: Vector equation of line

Q: a) Find the value(s) of c for which the following vectors vị = ,v2 = --- 1 and v4 are linearly…

A: According to our guideline we are supposed answer only the first question if you want any particular…

Q: If a = i+ 4j + k and b =i+ 8j +k, find a unit vector with positive first coordinate orthogonal to…

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Q: Find the indicated vector. Let u = 3i, v = i+j. Find 6u + v. %3D Oi+ 19j 19i + j 19i + 6j 11i +j

A: Given:       u=3i, v=i+j

Q: Find the area of the parallelogram spanned by vectors v and w suchthat ||v||=||w|| = 2 and v · w =…

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Q: Express the vector t as a linear combination of the vectors u, v, and w. 1 - 2 4 t = 0 , u = 5 , v =…

A: We use the definition of the linear combination of vectors to answer the given question.

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 coordinate vector of w relative to the basis S = {uj, u2 } for R2. uj = (12, – 12), u2 =…

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Q: Find the component form of the vector v and (b) sketch the vector with its initial point at the…

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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: Write the vector x=0 as a linear combination of the vectors u=0, v= 1, w= 1 1

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Q: Consider linear independent vectors v=(a,b,c) & w=(x,y,z) in R. Let be a linear combination of i &…

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Q: Consider the vector v = (−1, 3, 0, 4). Find u such that (a) u has the same direction as v and…

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Q: Find b so that the vectors v = i + jand w = i + bj are orthogonal.

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Q: Find a vector orthogonal to both given vectors u and v . u=2i-3j +k  v= -3i +4 j +4k

A: Given, u=2i-3j +k  v= -3i +4 j +4k    We have to find the orthogonal vector to both given vectors u…

Q: The vector y which is collinear with the vector u= and satisfies the condition u.v= 3, is O O O…

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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: let u = [-3, 4] and v = [2, -5]. Find (a) thecomponent form of the vector and (b) its magnitude. u +…

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Q: If the vectors u and v are linearly independent with au + bv = 0 then a = b = 0 O a = 0 and b # 0 0…

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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: let u = [-3, 4] and v = [2, -5]. Find (a) thecomponent form of the vector and (b) its magnitude. 3u…

A: u=-3, 4 & v=2, -5 a). 3u-4v=3-3, 4-42, -5=-9, 12-8, -20=-9-8, 12--20=-17, 32

Q: let u = [-3, 4] and v = [2, -5]. Find (a) thecomponent form of the vector and (b) its magnitude. 5v

A: Given that u=-3, 4  and  v=2, -5. This implies that, 5v=5·2, -5=5·2, 5·-5=10, -25 Thus, the…

Q: Consider the vectors y= 3i + 4j + 5k and w= i + j + k. Express the given vector in terms of i, j and…

A: The given vectors v=3i+4j+5k and w=i+j+k

Q: Find the magnitude of vector v. Y -2 w X

A: We have to find the magnitude of v

Q: Find the coordinates of the point P on the line and a vector v parallel to the line x = 3t, y = 1 –…

A: Given parametric equation of line x=3t, y=1-t, z=3+5t

Q: If a = i+ 10j + k and b = i+ 11j+ k, find a unit vector with positive first coordinate orthogonal to…

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

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: Q/ B/ If vector A = 3i – 2j + 7k and B = -i+j- 3k , find the area of triangular between vector A and…

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Q: (1b) Find vectors v and w such that v is parallel to y, w is perpendicular to y, and x = v+ w.

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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 ||u|| for the given exercise, and give a unit vector in the direction of u.

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Q: (1b) Find vectors v and w such that v is parallel to y, w is perpendicular to y, and x = v + w.

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Q: H.W 9- Given that a = (1,1) and b = (-1,0). Find a vector in the same direction as but a+b %3D %3D…

A: Given: a→=1,1, b→=-1,0 To find: A vector in the same direction as but a→+b→ five times as long.

Q: Find the vector z, given that u = ⟨1, 2, 3⟩, v = ⟨2, 2, −1⟩, and w = ⟨4, 0, −4⟩.      z = u − v + w

A: Given:                                                          u = <1, 2,…

Q: Let y = U = write y as the sum of two orthogonal vectors, one in Span {u} and one orthogonal to u.…

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

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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: Þ(x, y, z) = e¬x²-y²-z²+2yz

A: First take gradient and magnitude of gradient