If a = i+5j + k and b = i+ 9j +k, find a unit vector with positive first coordinate orthogonal to both a and b. * i+

Q: When analyzing the vector To the sum of two vectors, the first is parallel to the vectorA 2i-j+ 3k…

A: I am attaching image so that you understand each and every step.

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

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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: Express the vector in terms of it's length and direction. i + 2j - k

A: Solution:Given   i+2j+kTo express in terms of its length and direction.u=vvand v=vu

Q: Find the two unit vectors orthogonal to both a = (3, 1, 1) andb = (−1, 2, 1).

A: Given: a=3,1,1 and b=-1,2,1

Q: Find a unit vector that is orthogonal to both u and v. u = (-8, -6, 4) v = (12, -16, -2)

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Q: Find the unit vector in the same direction as the vector u = [8, –7].

A: When you divide a vector by its magnitude you get an unit vector along its direction.

Q: If a vector gets multiplied by a positive number, its direction will be *.reversed FO TO

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Q: Find a vector that has the same direction as 8i-j+4K but has a length of 6

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Q: 3. Find a unit vector with the same direction as (3, 4).

A: If we devide each component of vector v by |v| we will get the unit vector Uv.

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

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Q: Suppose that uj and u2 are orthogonal vectors, with u1 = 2 and u2|| = 4. Find |5u1 - u2 ||. ||5u1 -…

A: We have to solve given problem: Let  U1=(a1,a2)  U2=(b1,b2)5U1-U2=5(a1,a2)-(b1,b2)…

Q: Find the value of  x  so that the two vectors  (27,1,13)  and   (x,0,1)  are orthogonal

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Q: A vector u is a positive multiple of . Vector v = with a , what will be the signs of d, e, and f?…

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Q: Express the vector from P(-1, -4, 6) to Q(1, 3, -6) as a position vector in terms of i, j, and k.

A: Given vectors are P-1,-4,6 and Q1,3,-6.

Q: Find a unit vector in the direction of u = (3, 4, 5).

A: Given vector, u=3, 4, 5

Q: If a vector is expressed in terms of i and j, explain how to find the scalar multiplication of the…

A: The vector quantity has both magnitudes as well as the direction. if we multiply a vector by a…

Q: 1. The vector in the opposite direction to u = = (-1,0) and of half its length is

A: Explanation: Given that,  Vector u=-1,0 find the length of this vector  length of vector u =…

Q: Find a unit vector that is perpendicular to both ủ = (2,1, 2) and v = (2,– 2,– 1).

A: Given, u→=2,1,2 and v→=2,-2,-1 we are asked the unit vector that is perpendicular to both.

Q: What is the length of the vector whose initial point is (0, 1, -2) and (2, - 2, 3) 35 A. 38 В. V35…

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Q: 2. Find two unit vectors orthogonal to both and .

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Q: 3 Determine the unit vectors that are nernendicular to A - and R -

A: Perpendicular vectors

Q: Sketch the vector b = <3, 4> based at P = (−2, −1).

A: Sketch the vector b=<3, 4> based at P=(−2, −1).

Q: Find a unit vector that is orthogonal to both u and v. u = (-8, -6, 4) v = (17, -18, -1)

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Q: Find two unit vectors orthogonal to a = (-2, 1, 0) and b = (-4,0, 1)

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Q: Find the following vector. The vector in the direction of (24,10) with length 2

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Q: Find a unit vector parallel to the vector a´. a'= (-2,3,–1)

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Q: ) Find a unit vector with the same direction as (1,0, 7).

A: We can find the unit vector as below.

Q: If ï = (, 2), find a vector i that is perpendicular to ū.

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Q: Express the vectors in terms of their lengths anddirections. 2i - 3j + 6k

A: The given vector is a=2i-3j+6k. Compute the length of the vector as follows. a=22+-32+62=4+9+36=49=7…

Q: Find a unit vector in the direction of u = (5, 3, 2).

A: Given vector is u=(5,3,2) Find a unit vector

Q: Find the two unit vectors orthogonal to both a = (4, 1, 1) and b = (-1, 4, 1).

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Q: Find two vectors in opposite directions that are orthogonal to the vector        u = ⟨3, 1, −2⟩

A: u=3, 1, -2 Let v=a, b, c be the vector orthogonal to the vector u=3, 1, -2. Then, u·v=0…

Q: Find a unit vector that is orthogonal to both u = (2, -8, 6) and v = (4, 10, -6).

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Q: Find the vector W which is of length 6 and oppositely directed to u = (2,-2,1)

A: Given,          The vector w→ which is of length 6 and oppositely directed to u→=<2,-2,1>.

Q: If the magnitude of the vector u is √2 and its direction is 225°, then its components are:   (1,…

A: Solution of question as follows

Q: Find the magnitude of the vector AB A=(-2,3) and B=(3, - 4)

A: A vector has both magnitude and direction. The direction of a vector is indicated by an arrow.…

Q: What is the resultant of vectors a and b? (

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Q: Find the vector projy 2i - 2j - 4k, u = 5i - 12 k

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Q: i. What are the lengths of the x- and y-components of this vector? 10

A: Find your answer below

Q: Find the unit vector that has the same direction as vector v that begins at (0, -3) and ends at (4,…

A: If a vector is of the form ai^+bj^   then its unit vector along the direction v is written as…

Q: Describe a unit vector in R^3 with the same direction as <1,0,7>

A: Consider the given point vector

Q: Find a vector a that has the same direction as (-10,7, 10) bưut has length 4.

A: In the given problem we have to find a vector a that has the same direction as -10, 7, 10 but has…

Q: Find a unit vector that is orthogonal to both u and v. u = (-8, -6, 4) (10, -12, -2) %3D V =

A: Find the unit vector that is orthogonal to both u and v

Q: Find a vector orthogonal to the vectors ā = and 5=.

A: Recall:  Vector orthogonal to the vectors a→ and b→ is a→×b→a→×b→ We have, a→=1,2,3, b→=1,0,1