The contrasts (-3, 1 1 1) and (0, 0 , -1, 1) are orthogonal? Is it True or False?

Q: The vector that has the same direction as ⟨3,4,3⟩ but has length of 4 is

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Q: Explain how the direction vectors of two lines in ℝ3 can be used to determine whether the two lines…

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Q: The image of (-2 , 5) under reflection y = -x followed by translation with translation vector (-3 ,…

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Q: The vectors (3,-4,1) and (5,3,3) are orthogonal. True False

A: Topic - vector

Q: What position vector is equal to the vector from (4.-3. - 2) to (-5, -8,7)? The position vector is…

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Q: Find b and c so that  (9, b, c)  is orthogonal to both  (1, 2, 7)  and  (1, −2, 1).

A: To find b and c so that (9, b, c) is orthogonal to both (1, 2, 7) and (1, −2, 1).

Q: What position vector is equal to the vector from (3, 5, -2) to (0, -6, 3)?

A: We have given two vectors;  (3, 5, -2) , (0, -6, 3)

Q: The line through the point (0, 1, 1) that is orthogonal to both ⟨0, -1, 3⟩ and ⟨2, -1, 2⟩.

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Q: The two vectors a = (-1,2,-2) and b = (2, -4,-5), are not parallel but are orthogonal. Select one:…

A: Using algebraic operation

Q: Find two vectorsī and 02 whose sum is (2, –4), where v, is parallel to (2, -4) while vz is…

A: We have to find vector v1 →and v2→   the sum of vector v1 →and v2→ is 2, -4   vector v1 →is parallel…

Q: Do the vectors (1, 0, 0), (0, 1, 0), and (2, 3, 0) lie on the same plane? Briefly explain how you…

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Q: 10

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Q: Find a direction vector for the line containing the origin (0, 0, 0) and the point (2, 3, – 1).

A: The given points are 0,0,0  and  2,3,-1

Q: as the sum of two orthogonal orthogonal to ư

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Q: Find ||u||, ||v ||, and ||u + v||. -(-1. 금), v-(2.-3) v = (2 - ± ) u = 4 (a) ||u|| (b) ||v|| (c) ||u…

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Q: If vectorAB =-7i + 3j + 8k and A is the point (-2, -3, 6), find B.

A: Given : AB =-7i + 3j + 8k and A=(-2, -3, 6)

Q: Find a direction vector for the line through (4, 5, 3) and (2, – 3, – 1).

A: to find the direction vector

Q: Find the symmetric equations of the line that passes through the point (3,6, –10) and is parallel to…

A: The line passes through a point means that the point lies on the line. The direction vector of a…

Q: Every vector of R²is linear combination of (-1, 1), (2, –2)? Justify

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Q: Give an example of a non zero vector that is perpendicular to (5,7,4)

A: We know that "two vectors are perpendicular to each other if and only if their dot product is zero"…

Q: The scalar equation of the line perpendicular to (x, y) = (5, 2) +r(1, -3) through the point (2, -2)…

A: The scalar equation of a line is of the form Ax+By+C=0

Q: Determine whether u= (-1, 11) is a linear combination of x =(1,3) and y=(2,-1).

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Q: The line that passes through the point (4, -2,0) and parallel to the vector (1, 2, –3) has symmetric…

A: The solution is given in the next step.

Q: Find the symmetric equation for the line through the point of (2.-5,4)and a vector (3,–1,-3).

A: Given the vector is, 3,-1,-3 And the point is, (2,-5,4). The parametric equation for…

Q: Determine which vectors that are orthogonal to (-3,- 6)? (-4,2) and (- 1,3) (-10, 5) and (-3, 6) a.…

A: Since your question has multile question we will solve the first question for you.   Find the…

Q: Suppose L(5, 4) was reflected across the line y = x then translated along the vector . What is the…

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Q: Then Duf(4, -3) in the direction of the vector 20 (-1, –2) is Let f(x, y):

A: Answer is mentioned below

Q: Let vector AB = (2,3,1). If the coordinates of A are (2,1,5), what are the coordinates of the point…

A: Vector AB= B-A

Q: a) Find an equation of the line through P(1,-2,4) with direction vector v=[2,4,-4]

A: To find the equation of line.

Q: Express the vector (-1,5,-6) in R^3as a linear combination of (2,0,7),(2,4,5) and (2,-12,13).

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Q: What is the component form of the vector whose tail is the point (-1,5), and whose head is the point…

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Q: What is the component form of the vector whose tail is the point (-2, 6), and whose head is the…

A: Answer is in step 2.

Q: Let L, be the line passing through the point P-(1, -7, 5) with direction vector d-[1,-2, 0], and let…

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Q: Find the equation of the plane that passes through the point (−2, 8, 4) and contains vectors ⃗a…

A: The equation of plane passing through the point x0, y0, z0 and contins vector a→ amd b→ is n1(x -…

Q: The vector equation for the line passing through the points (-4, 1,0) and (4, 4,-3) is r(1)-

A: It is given that the line passes through the points (-4,1,0) and (4,4,-3). Consider that the vector…

Q: Find symmetric equations for the line that passes through the point (5, -2, 7) and is parallel to…

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Q: If you were to translate the coordinates of point C using vector (-3,2) , what would the coordinates…

A: Here we can find the answer as below.

Q: The vector (1, 0, 0) makes a 45 degrees with the vector (x, y, z). What is the relationship between…

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Q: The vectors (8, 6) and (k, 12) are parallel. What is the value of k

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Q: What is the component form of the vector whose tail is the point (-3, 2) and whose head is the point…

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Q: Is it possible to write the vector (-5,11,-7) as a linear combination of the vectors…

A: See the attachment

Q: 1. For the cross product between vectors a=[h, -1, 8] and b=[k, 5, 7] to be axb= [-47, -5, 17], what…

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Q: Find the equation of the plane through the point (-3,2,0) and perpendicular to the vector (1, -2,5).…

A: Questions from vector calculus.

Q: The vectors (-3,4, -1) and (3, -4,1) are orthogonal. True False

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Q: If vector (3,2,2) is expressed by a(1,1,-1)+b(0,1,3)+c(1,-1,1), what are the values of a, b, and c ?

A: Given : Vector (3,2,2) is expressed by a(1,1,-1)+b(0,1,3)+c(1,-1,1). That is

Q: What is meant by orthogonal?

A: Orthogonality is a property synonymous with perpendicularity.

Q: Determine the vector equation for the line that is parallel to = [1,5,-7]+[2,-1,5] with the same…

A: The general equation of line in vector form is    .Then note the result : Line passing through the…