53. Given v = 4i + 9j and w = 2i – j, a. Find proj,v. b. Find vectors v and v2 such that vị is parallel to w, V2 is orthogonal to w, and v, + v2 = v.

Q: For each of the following pairs of vectors z and w, compute (i) ||z||, (ii) ||w||, (iii) z,w||, and…

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Q: Use the given vectors u = 5i-4j to find u. W W = -2i - j

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Q: Show that the lines L1 : x = 4 – t, y = 2t, z = 2+t and L2 : x = 1+ 4t, y = 3 – 8t, z = 5 – 4t are…

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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

Q: If v . w = 0, then the vectors v and w are________.

A: Lets two vector be v and w. v.w = v × w × cosθ Where theta is angle between v and w.

Q: 2. For the vectors u = -5i + k and v = 3j - 4k, find a. (u · v)u b. u - 3v

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Q: Find the length and direction (when defined) of u x v and vxu. u= 5i + 3j – 5k, v=0

A: we know that  uxv=|u|.|v|sin∅.n^where ∅ is angle between u and v and n^ is unit vector perpendicular…

Q: Given the vectors U =i- 2j +k, V = 2i +j+k and W = 3i - j+2k, compute the following: (a) Ux V (b)…

A: We will apply dot product formula and cross product formula.

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: Find the length and direction (when defined) of u xv and v×u. u= - 8i – 4j – 3k, v = 3i + 3j + 4k

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Q: 11. Use vectors to show that the distance from P:(x1, yı) to the line ax + by = c is |ax, + by, – c|…

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Q: If v . w = 0, then the two vectors v and w are____

A: If v . w = 0, then the two vectors v and w are____

Q: 1. Compute the following for the vectors in R3, x [1 3 21T and y [40 1T y and y x (a) (b) 2 and y2…

A: From the given information, [1 3 –2]T and [4 0 –1]T.

Q: 1. Given the vectors U = i – 2j+k, V = 2i+j+k and W = 3i – j+2k, compute the following: (a) U. V (b)…

A: Given vectors   u = i^ - 2j^ + k^  ,  v = 2i^ + j^ + k^and w = 3i^ - j^ + 2k^We find a u.v b u×v c…

Q: Find the length and direction (when defined) of u x v and vxu. u= - 12i + 9j – 12k, v = - 4i + 3j –…

A: Using formula of u x v and v x u,

Q: Given vectors u = 2xi + 9j and v = xi - 4j, find x so that u and v are orthogonal.

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Q: Suppose vectors v, w, and z sum to the zero vector. If v = 8.2i - 3.8j and w = 4.1i + 1.3j, find z.

A: We have to solve

Q: 3. Find the angles between the vectors: u = 2i + j, v= i + 2j – k а. b. u = 2i – 2j + k, v = 3i + 4k

A: Angle between two vectors, θ=cos-1u→.v→|u→| |v|→ a)  u→.v→=2i+j.i+2j-k       =2+2 u→.v→=4 |u→|=22+12…

Q: Decompose V into in two vectors V1 and V2, where V1 is parallel to W and V2 is orthogonal W. V=2i+j…

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Q: Given v = 2i + 4j, w = -3i + 6j, find projw v. Then decompose v into two vectors, v1 and v2, where…

A: *The given vector v is, v=2i+4j *The vector w is, w=-3i+6j The projection of the vector on the other…

Q: d) Prove that ||vxw||²+|v-w[? = ||v||²|w||² for all vectors v, w in R3

A: Prove the following

Q: Given v = 2i + j, w = 6i + 3j, find projw v. Then decompose v into two vectors, v1 and v2, where v1…

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Q: If y is orthogonal to the vectors u and v, then y is orthogonal to u+ 3v. True False

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Q: Given the vectors vi = (1,1, –1), v2 = (1,2,3) and v3 = (0,1,1). S = { v1, v2, v3} set R3 does it…

A: 3 vectors span R³ if they are linearly Independent. Vectors are linearly Independent if their…

Q: Given v = - 7i + 5j and w= -i+j, a. Find projwv. b. Decompose v into two vectors v, and v2, where v,…

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Q: Suppose that u and v are unit vectors in R°. If the angle between u and v is T/4, then what is the…

A: Given that vectors u and v are unit vectors and angle between vectors u and v is π4.  We know that…

Q: If v.w 0, then the vectors v and w are

A: We know that two vectors u and v are said to be orthogonal if u . v = 0.

Q: Given the vectors v = 4i + 2j + k and w= 2i + 3j - 4k. Find | 2v – w|

A: Given vectors V=4i+2j+K W=2i+3j-4k Now we have to find |2v-w| as shown below

Q: 42. Show that the unit vector ī = xỉ + yj is not parallel to ū = yi – xj for any choice of x and y.

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Q: Given the vectors v = 4i + 2j +k and w = 3i – 4j + k. Find | 2v – w |

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Q: For what value of c is the vector v = ⟨2, -5, c⟩ orthogonal to w = ⟨3, 2, 9⟩?

A: Two vectors are said to be orthogonal if their dot product is zero.

Q: ind the value of a so that vectors U = ai + 9j and V = 3i + 3j are

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Q: Given that the vectors ở = (1, 2– k,3) and b = (7, 4, k+2) are perpendicular, what is the value of…

A: Given vectors are: a→=1,2-k,3 and b→=7,4,k+2

Q: For two nonzero vectors u and v, if u v=0 then u and v are parallel.

A: Given that u and v are two nonzero vectors   Dot product of two nonzero vectors u.v=|u|.|v|…

Q: what is u.v when u and v are two unit vectors with an angle of (pi/6) between them. if u=i and if v…

A: Given: u=i, angleθ between u and v=π6 let's assume v=xi+yjx2+y2 we know that angle between two given…

Q: Given the vectors v = 4i + 2j – 3k and w = 3i – 4j + k. Find | 2v – w | V

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Q: Given v = 3i - 2j, w = 2i + j, find projw v. Then decompose v into two vectors, v1 and v2, where v1…

A: Given that, The vectors  v = 3i - 2j, w = 2i + j. We have to find projw v By using a formula, projw…

Q: Q2/ If A=ai+bj+3k, B= 2i+3j+4k, C-i+j+6k are vectors , perpendicular to B and A is perpendicular to…

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Q: A line L has a direction vector v = 2i t 4j+ v5k and passes through the Find the distance between…

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Q: 5. Let A =-ai+3j–2k and B = 4i + ßj+8k (a) Find a and ß if A and B are parallel. (b) Determine the…

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Q: 98 25) Gvon vectors v= 30tj and w=-2i -j. Decompose v into two vectors V, and Vz, where V, is…

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Q: If v = 5i + 4j and w = 6i - 9j, find the vector v +w.

A: The vector given are v=5i+4j and w=6i-9j. To find: the value of v+w. Solution: the sum of both…

Q: d)) Find the angles between the vectors. .u = 2i + j, v =i+ 2j – k Lu = 2i – 2j + k, v = 3i + 4k u =…

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Q: Consider the two vectors A = Axî + Ayĵ and B = Bxî + Byĵ. If î · î = ĵ • ĵ = 1 and î · j = ĵ · î =…

A: Note: As per bartleby instruction when more then one question is given only one has to be answered.…

Q: given vectors u=4i-j and v= 3i+3j compute the projection of v onto u?

A: Given, vector u and v

Q: O Are the three vectors: V= 4i-8j+kV= 2i+j-2k and ū;=3i-4j+12K in the Same Plane?

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Q: Given v = 6i + 2j and w =i-j, a. Find projwv. b. Decompose v into two vectors v, and V2, where v, is…

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Q: If v = 5i + 6j and w = 10i + 12j, find proj,v. Then decompose v into two vectors v, and v2, where v,…

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Q: For what values of y are the vectors yi – 2j + 3y k and 6i +j+ 3y k orthogonal.

A: To find the values of y for which the vectors yi-2j+3y k and 6i+j+3y k are orthogonal.

Q: Prove that in R², the vectors {v1, v2, V3} are always dependent. What about if we have two vectors…

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