Let P be the point (1, –3, 0) and ū be the vector ī = (-3, 6, 2) %3D • Find the point 1 unit away from P and in the direction of ū. • Find the point 2 units away from P and in the opposite direction of v.

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

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Q: 27. Find a unit vector that is orthogonal to both i +j and i+ k.

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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: Decompose v into two vectors, v1 and V2, where v is parallel to w and v2 is orthogonal to w. v=i+j,…

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

Q: Let DE be the vector with initial point D(8, 6) and terminal point E(-1, 5). Write DE as a linear…

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Q: Find the distance of point A(23.2) from the line that passes through the origin and parallel to the…

A: given point A 23 ,2 and line passes through orgin and parallel to the vector v =<1,3>

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: 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: 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: Let y be the vectors:     Determine      1) The length of v   2) The value of u*v   3) The…

A: Since you have posted a question with multiple subparts, we will solve first three subparts for you.…

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

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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: c) Find a vector, AB , with magnitude 4 in the direction of PQ where P and Q have coordinate (5,0,8)…

A: Find a vector, AB, with magnitude 4 in the direction of PQ where P and Q have coordinate (5, 0,8)…

Q: Find the vector z, given that u = , v = , and w = . z = 8u - 3V - -W 2 1. Z =

A: We have been given the vectors  u = <1, 2, 3> v = <2, 2, -1> w = <4, 0, -4>

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 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: Which of the following vectors are equal to j × i?(a) i × k

A: We know that, i×j=k Therefore, j×i=-k Hence the answer.

Q: W 2-Find a vector that is perpendicular to both B = i +j-k B = 4i – j 1. A = 2i +7j – 4k | > 2. A…

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Q: Find the unit vector u in the di rection of the vector v=4 (2, 1, 2) 1 U = OA 1 U = 1 Oc. 12 OD. 1 u…

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Q: Find the components of the vector ī, with |u| = 7.8 and 0 = 21.3°.

A: Given: To Find:  The components of given vector  Formula Used: The components of vector v with…

Q: Find the component form of the vector v given ||v|| = 12 following the direction of u (3, –5)

A: Find the component form of the vector v given ||v|| =12 following the direction of u = (3,-5)

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.

Q: Find the coordinate vector of w relative to the basis S = {u1, u2} for R2. : (6, – 6), u2 = (2, 2);…

A: Here we have to find the coordinate vector of w relative to the basis S ={u1,u2} for R2 . Here…

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

Q: Find the component form of the vector v given ||v|| 12 following the direction of u (3, –5) %3D

A: The vector v in direction of u can be found  blew step.

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

A: We have to find the magnitude of v

Q: Find a unit vector orthogonal to the vector A= 2i-j+k and parallel to the vectors B= 2i+2j and C=…

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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: 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: Let v be the vector The vector of length 3 in the opposite direction as v is 2 Select one: a. -2 O…

A: Vector v  = (1,2,-2) opposite direction to  given vector can be find as -v (-1,-2,2)

Q: If a = i+ 8j + k and b = i+ 13j + k, find a unit vector with positive first coordinate orthogonal to…

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Q: Let v be the vector . The vector of length 5 in the opposite direction as v is Select one: a. 5 -5…

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Q: Find a unit vector e, where v = (4,2, 5) ey = %3D

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Q: Find a unit vector orthogonal to both u and v.u = 3i + j v = j + k

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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 the angle e between the vectors. u = (0, 0, 1, 0), v = (3, 3, 3, 3) radians

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

A: Cros product of two vector give third vector which is perpendicular to both vectors.

Q: Find the distance of point A(2/3,2) from the line that passes through the origin and parallel to the…

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Q: (b) Find the direction e of the vector u = .(angle between the positive x-axis and the vector)

A: Topic = vector

Q: Þ(x, y, z) = e¬x²-y²-z²+2yz

A: First take gradient and magnitude of gradient

Q: Let v be the vector from initial point P, to terminal point P,. Write v in terms of i and j. P1 =…

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Q: Let r (t) = |r (t)| = ( the length of the vector is round to one decimal

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

A: Given : a=i+4j+k and b=i+8j+k.