20- vectors U = i-3j %3D V= 2 + 3j a) 2(4)- 3 (v) b) - 3j)2+3j) 2 (i -3j) 3(2i+ 3j ) 15 4i+ C) Find a unit vector in The same direction as V

Q: 4. Use vector methods to find (a) the area of the triangle ABC where A(-2, -1, 1), B(3,-2, 1) and…

A: (a) Given vertices of the triangle are A(-2,-1,1) , B(3,-2,1) and C(1,3,-2)

Q: 4. (a) Find the unit vector that has the same direction as (3,4,0). (a) Calculate the distance…

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

Q: u and i are vectors of R" such that ||ū|| = 3, |||| = 4 and the angle between them is. Determine the…

A:

Q: Find the angle 0 between the vectors. u = (1, 1, 1), v = (7, -6, 5), (u, v) = u1Vı + 2u2v2 + U3v3…

A:

Q: 10 Find the vector equation of a line whose symmetric equations are z-1 y+3 %3D 3. -4 Express your…

A: To find the vector equation of a linewhose symmetric equations are   x-12=y+33=z-1-4.

Q: (2) Express the vector ū = < 3, 2 ,7) as a sum of a vector parallel to DC ond a vector perpendicular…

A: Consider the points A-2, 3, 1 , B0, 0, 2and C-1, 5, -2. We have to solve the following :…

Q: Find the angle (in radians) between the 2 vectors U(-3, 4, -4) and V(1, 2, 2)

A: Given vectors are,               U(-3, 4,-4 ) and V(1, 2, 2 )

Q: 5. Determine the value of a so that the vectors v = perpendicular. (a,3, -2) and v - (2, -2a, 1) are

A: Solve the following

Q: I\ Find the unit vector that has the same direction as vector v = -4i - 3j + 6k ? %3D

A:

Q: Q / Determine the value of b so that vectors 4 = 49-593 V=-2₂0₂-5 w=bs 1, 6 lg are in the Same Plane

A: We have given that the vectors ,  u = 4 , -5 , 3  ,  v = -2 , 0 , -5  ,  w = b , -1 , 6 We know that…

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

A:

Q: 4. Find a unit vector that points in the same direction as v = (1,3,9).

A:

Q: 10. Find the vector equation of a line whose symmetric equations are x-1 y + 3 z- 1 %3D %3D 3…

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Q: Find the angle between the vectors u = (1, −1) and v = (0, 1).

A: Given query is to find the angle between the vectors.

Q: 11) Use properties of vector to determine the value of the dot product å. b for the vectors ở = 21…

A:

Q: 4. Find a unit vector in the same direction as the vector 8i- j+ 4k.

A:

Q: 3. The line through the point (2, 2.4, 3.5) and parallel to the vector 3i+ j – k Answer + (2i+ 2.4j…

A:

Q: Let the vector 3i +j can be expressed as a sum of vectors u and v where u is parallel to the vector…

A:

Q: Find the angle θ between the two vectors.u = (3, 3), v = (−2, 2)

A:

Q: Two vectors of magnitudes B= 5 and C = 3 are lying on the xy plane as shown in the figure. What is…

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Q: 24. Verify the parallelogram law for vectors u and v in R": |u + v|l° + |[u – v||² = 2||u||² +…

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Q: 2.) Find two vectors that are orthogonal to the vector v = 8i - j

A:

Q: Find the angle θ between the vectors.u = (1, 1, 1), v = (2, 1, −1)

A: The vectors are To find the angle between the given vectors, use formula

Q: 8-b. Find the real part of the length of the vector v° = (5 + i, –2 + 2i, –1+i)

A:

Q: 2. Express the vector v = 3i – 4j as the sum of a vector parallel to b = 2i +3j and a vector…

A: Given, v→=3i^-4j^ The parallel vector c→ to the vector b→=2i^+3j^ can be written as c→=λb→=2λi^+3λj^…

Q: 1. The vector x expressed in terms of the vectors w and u а) w — и с) w + u b) и — w м.п (р

A: …

Q: 4. Using the vectors: ü=[2,-1,3], v=[4,5,-2], w=[1,-1,7], calculate: a) b) ux v c) ū+ v +2w

A: Here we have to perform the vector operation

Q: Find the angle θ between the two vectors u = (1, 2, 1) and v = (2, 1, −1).

A:

Q: Q/ find all unit vectors parallel to the yz plane and perpendicular to the vector V= 5i - j + 2k ?

A: Given,   A vector V= 5i - j + 2k.

Q: wher analyzing the vector Ā szi-j +3k to the sum of the vectors The Sirst is Parallel to the vector…

A:

Q: Find the angle θ between the vectors.u = (1, −1, 0, 1), v = (−1, 2, −1, 0)

A: The given vectors are, u = (1, −1, 0, 1), v = (−1, 2, −1, 0)

Q: B- If you have a vector perpendicular to the plane of P(1,-1,0) , Q(2,1,-1) nd R(-1,1,2) find: 1. PQ…

A: Given P(1,-1,0), Q(2,1,1) and R(-1,1,2)

Q: 5) Find a unit vector that has opposite direction of the vector i - 2j + 4k.

A: First change direction of vector then find magnitude and write unit vector

Q: Two vectors of magnitudes A=3 and B=3v2 are lying on the xy plane as shown in the figure. What is…

A:

Q: a. Without doing any calculation, explain why one might conjecture that two vectors of the form (a,…

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Q: 7. Let u and v be two vectors for which ||u||² + ||v||² = ||u + v||² From this information alone,…

A: Given that u2+||v||2=||u+v||2 consider the right hand side of the given equation. ||u+v||2=u+v.u+v

Q: -8 Find the area of the triangle which is defined by vectors u = and v = -3 Area =

A: Solve the following

Q: Q3 find 1)angle between two vector. 2)projection of vector A&B. A = 2i + 2j - K B = 4i-6j + 4k

A:

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 the two unit vectors orthogonal to both a = 3j + 2k and b = -i- 2k. O A -61 - 2j + 3k and 6i+…

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Q: Find the angle θ between the vectors.u = (−4, 1), v = (5, 0)

A: u = (−4, 1), v = (5, 0)

Q: Three vectors are defined by position vectors defined as ā = 2i+ j-3k, b = -3i+2j- 4k and č = xi+…

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Q: Find a unit vector orthogonal to both u and v. u = -3i - 2j - 5k li 1 3i+ -j + 4 10 V = - 2

A: To find A unit vector orthogonal to both u and v

Q: 8 Find the 3-dimensional unit vector in the direction: a 2i + 3k 6 -i+ 2j – k c 2i – 2j + k

A:

Q: (B): Find the unit vector perpendicular to the vectors: 3i - 4j+5k 4i + 5j-6k (PUBIEN

A:

Q: vector. 19. —3і + 7j 20. (-4, 2, 4) 21. 8i – j + 4k |

A:

Q: 3-a. Find the area of the triangle determined by the points P, Q, and R. b. Find a unit vector…

A: Given points P(1,-1,2)  Q(2,0,-1)  R(0,2,-1) (a) The objective is to find the area of the triangle…

Q: b) Find two unit vectors that are perpendicular to both vectors i = (2,0,–1) and ỹ = (-3,–4,1). Are…

A: The cross product of two vector is perpendicular to both of the vectors. The cross product of the…