Find vectors that satisfy the given conditions: 1. The vector in the opposite direction to u = (1, –2) and of half its length is

Q: Find the vector v with the given length and the same direction as u.||v|| = 4, u = (−1, 1)

A: To find a vector v with the given magnitude of ||v|| = 4 and in the same direction as u = (−1, 1).

Q: Find the unit vector in the direction of v and verify that it has length 1.

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Q: The unit vector which is perpendicular to both r1=8ax+3ay- 2az , r2=2ax+7ay-6az is equal to

A: Given, vectors arer1=8ax+3ay-2az, r2=2ax+7ay-6azThe unit vector perpendicular to both vectorsr1, r2…

Q: Find the vector with the given length || v || = 3, and in the direction of u = (0,2,1, -1)

A: Sol

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 ||7e – 4f|l, assuming that e and f are unit vectors such that ||e + f|| =

A: Suppose e and f be the unit vectors such that e+f=32 First, find the dot product of the vector e…

Q: Find in terms of i and j the following vectors :

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Q: The unit vector which is perpendicular to both r138ax+3ay-2az, * r2=2ax+7ay-6az is equal to a)…

A: As per our guidelines, we are allowed to answer only question. Since, you have posted multiple…

Q: find the acute angle between the given linesby using vectors parallel to the lines. 2 - x + 2y = 0,…

A: 2-x+2y = 0⇒2y = x-2⇒y = x-22⇒y = x2-1             --(1)So, vector parallel to (1) is a→ = 12i ,…

Q: given two vectors v m which are perpendicular. under which condition is V+W perpendicular to V-W?

A: Since vectors v and w are perpendicular so, their dot product is 0

Q: Find ||e − 4f||, assuming that e and f are unit vectors such that ||e + f|| = √3.

A: The step-by-step solution to the given question is ..  we have ,  e+f=3..........(1) we have to find…

Q: 4. Find the vector v that is orthogonal tou=i+j+k and whose r-component and z-component are 2 and…

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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: For AABC, let b and c denote the vector AB and AC , respectively. The vector BH is orthogonal to AC.…

A: Orthonormal vectors are perpendicular to each other.

Q: Consider two vectors A and B prove that the cross product between them can be calculated as follows…

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Q: Find c so that the vector v is orthogonal to W = ||

A: Given: v=1c. w=2-1 Vector v and w are orthogonal only if the dot product of vectors is zero.

Q: Consider the vector v = (x, 2) in R2. If you rotate the vector by 90-degrees counter-clockwise, then…

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Q: For what value of t, if any, is the vector (4t, -1) parallel to the vector (4, -1) ?

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Q: Consider the vector v = 1 and the vector "function" w(k) = 1 For what value of k are i and w(k)…

A: Two vectors v→ and w→ are said to be orthogonal if v→·w→=0 Given v→=111w→=11k

Q: Let b be a vector in R" satisfying the following equation. 4 3 =Db 7. Then m- and b

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Q: Find the components and length of the following vectors: i + j

A: Given vector is i+j. To find the component and length of the vector. Solution: In two-dimensional a…

Q: Find vector u with the magnitude given that satisfies the given conditions. v (7, -1, 3), ||u || -…

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Q: Sketch the following vectors, and find their components andlengths: i + j + k

A: The vector is i+j+k sketch the vector and find its length.

Q: In Fr let ej denote the vector whose jth coordinate is 1 and whose other coordinates are 0. Prove…

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Q: For what value of t,if any, is the vector (1, 4t) parallel to the vector (4, - 1)? Not OA. t = -2…

A: If the Vectors u and v are parallel then u=kV , K is any scalar.

Q: For what value of t , if any, is the vector (4t, -1) parallel to the vector (4, -1) ?

A: Given :4t,-1 and 4,-1

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: Is it true that if vectors a-b and a+b are orthogonal, then la|=|b|.

A: Given vectors a-b and a+b are orthogonal. The objective is to prove if vectors a-b and a+b are…

Q: At what value of k are these vectors collinear?

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

A: Given: u=123 v=231 The modulus of the vector u→ can be calculated as, u→=12+22+32      =1+4+9…

Q: In each part, find the two unit vectors in R² that satisfy the given conditions. 1. The two unit…

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Q: For the following pair of vectors, find U · V. U = 6i + 2j, V = −6i + 2j

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Q: Given the points X(1, -2, 1) and Y(0, 3, -2), find a vector that is collinear with XY and has a…

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Q: Find the value of c that will make the vector 2 lie in the span of 0 2 and

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Q: The vector i has length 11 and points at an angle of 15 The vector j has length 18 and points at an…

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Q: Given the following vectors: ü =, i = Find u x v.

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Q: For the following pair of vectors, find U · V. U = −7i, V = 9j

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Q: Given the points X(1, -2, 1) and Y(0, 3, -2), find a vector that is collinear with XY and has a…

A: Given: X(1, -2, 1) and Y(0, 3, -2).

Q: 1. Plot the following vectors using arrows on an xy-graph: -- (}). v-[+]. 1 u = V = 2u, u+v. Is…

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Q: Given the vector u (2, 2), find the magnitude and - angle in which the vector points (measured…

A: Given that: u→=2,-2. Therefore, magnitude of the vector is= u→=22+-22=22.

Q: Find the horizontal and vertical components of the vector with the given length and direction, and…

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Q: For any nonzero vector v, the unit vector that has the same direction as v is________ . To find this…

A: For any nonzero vector v, the unit vector that has the same direction as v: To find this vector,…

Q: For the following pair of vectors, find U · V. U = −2i, V = 9j

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Q: 2) With respect to the origin 0, the position vectors of points A, B, Cand D are given by OA = 1 OB…

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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 values of ( x ) such that the vectors and are orthogonal.

A: Given: The two vectors are: 3,2,x and 2x,4,x Also, the two vectors are orthogonal.

Q: Given the vector u= find |ū| and the direction of ủ.

A: We have the vector u→=-3,8. Then we have to find u→ and the direction of u→.

Q: Q2) Suppose a vector y is orthogonal to vectors u and v. Prove or give a counter example that y is…

A: Given that y is orthogonal to vectors u and v. To show: y is orthogonal to vectors u + v or not.

Q: For the non-zero vectors A and B to be perpendicular to each other, the necessary and sufficient…

A: Given, For the non-zero vectors A and B to be perpendicular to each other, the necessary and…

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

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