Find the measures of the angles of the triangle whose vertices are A = * .(-1, 0), B = (2, 1), and C = (1, -1). Use dot product of vectors

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

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Q: Find the area of the parallelogram that has the given vectors as adjacent sides. Use a computer…

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Q: How to calculate the cross products of vectors ? = {3,4,7} and ? = {4,9,2}?

A: GIVEN: Two vectors {3, 4, 7} and {4, 9, 2}

Q: Determine the volume of the box whose sides are the vectors (1, -2, 1), (2, 3, -2), (-1, 3, -2)

A: use determinant method to findout the volume.

Q: Find the shortest distance from point P = (1,2,-3) to the plane which passes through (2,3,-1) and…

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Q: Find area of triangle whose vectors Р (3,3, 1), Р2-1,0,2), Р3(2,3,3)

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Q: Two vectors are considered equivalent (equal) vectors if they and

A: Every vector quantity has dimension as well as mangnitude.

Q: Find the vector of length 2 making an angle of 60° with the x-axis.

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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 length of the cross product between the vectors k and -k is equal to the zero vector. Select…

A: Given that , the length of the cross product between vectors k and -k is equal to the zero is it…

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: The sum of the squares of the direction cosines of a vector in space add up to ..............

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Q: What is the area of the parallelogram formed by the two vectors = (1,5) and = (-3,-2)?

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Q: Find the vector with length V17 and same direction as = (7,0, -6).

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Q: Find the vector from the origin to the point of intersection of the medians of the triangle whose…

A: To determine the point of intersection of the medians of the triangle.

Q: It is possible for two nonzero vectors to have a dot product of 0. True False

A: Let u and v be two nonzero vectors

Q: What is the magnitude of the cross product of two parallel vectors?

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Q: 5. Calculate the area of the parallelogram formed by the vectors (4, 10, 9) and (3, 1, -2).

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Q: Find the vector that has the same direction as (6, 2, -3) but has length 2.

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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: Find the area of the parallelogram that has the given vectors u = ⟨2, −1, 0⟩,     v = ⟨−1, 2, 0⟩ as…

A: Given vectors as adjacent sides are u=2,-1,0, v=-1,2,0.

Q: Calculate the sum of the vectors that can be drawn as a vecto from the vertices of the triangle…

A: The vertices of the triangle is A7,4,-4, B1,-1,1 and C-8,-1,3

Q: Find the acute angle formed by two diagonals of a cube. (vectors) show complete solution.

A: It has been assumed that the length of each side of the cube is a unit.

Q: Express à = (3, 1, –1) as B + Č, where B is parallel to the vector (1, 4, 2) and Č is perpendicular…

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Q: Find the angle between the vectors (2, 1) and (3, -2) to the neareast second.

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Q: Find the distance of point 4(2-/3,2) from the line that passes through the origin and parallel to…

A: Distance of a point A(x1, y1) from the line ax+by+c=0 is given by d=ax1+by1+ca2+b2

Q: Compute for the cross product of the following pairs of vectors (-4, 3, 0) and (6, 2, -5). Then,…

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Q: why is it not all 4 vectors span W?

A: Lets look at how span of a set is defined :

Q: Find the vector of length 2 making an angle of 45° with the x-axis.

A: Find the vector from the given data

Q: Find the equation of the line that passes through the point (3,4,5) and is parallel to the vector…

A: The equation of a line that passes through the point: x0, y0, z0 is L=x0, y0, z0+ta, b, c, where a,…

Q: Find the area of the parallelogram that has the given vectors as adjacent sides. Use a computer…

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Q: Find the area of the parallelogram whose diagonals are represented by the vectors a = (3,-3,1) and b…

A: As we know that; The expression for the area of the parallelogram with the diagonals a→ and b→.…

Q: Find the sum of the vectors (3,0,1) and (0,8, 0) and illustrate geometrically.

A: Solved below

Q: Find the vector v in the plane represented by the directed line segment from (4,-3) to (-2,6)

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Q: Find the area of the parallelogram defined by the vectors ä= (2, -2,0) and 6= (0,1,2)

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Q: Find the area of a parallelogram with two sides identified by vectors from the origin to the points…

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Q: Find two vectors V1 and V2 whose sum is ⟨2,−5,3⟩, where V1 is parallel to ⟨4,4,0⟩ while V2 is…

A: Parallel vector will be multiple of each other  Perpendicular vector has dot products zero

Q: Find the volume of the parallelepiped determined by vectors , and

A: Find the volume of the parallelepiped determined by vectors <3,1,4>, <2,0,2> and…

Q: what Is the v product of two vectors a=C1,4)-2),

A: Which is a scalar quantity.

Q: Find two vectors vj and 2 whose sum is (-2, -5), where is parallel to (-3, 4) while vz is…

A: Solution: The objective is to find the vectors

Q: Find the area of the parallelogram defined by the vectors (9,1) , (-5,5)

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Q: Find a vector equation for the line segment from (2, -1, 4) to (4, 6, 1)

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Q: Find the angle between the vectors [ -1, 1, 2] and [2,1,-1].

A: Consider the vector: v = −1,1,2w =…

Q: find two unit vectors orthogonal to (-1,-1,5) and (-5,-,3,3)

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Q: The dot product of two vectors is also equal to the product of their __________ multi-plied by the…

A: The dot product of two vectors is also equal to the product of their __________ multi-plied by the…

Q: The dot product of two vectors is a ________ quantity. For this reason, it is some-times called the…

A: Let A and B be two vectors, the dot product is defined asA.B=ABcosθ, where θ is the angle between…

Q: Find two vectors and īz whose sum is (-4, -2), where vy is parallel to (-2, -5) while ū, is…

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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…

Magnitude

A vector is an element with both direction and magnitude. A vector is represented using an arrow, where the arrow represents the direction of the vector and its length is represented using the magnitude. The set of vectors in space is known as vector space. The vectors can be added, subtracted, multiplied, and divided in a vector space. The image below shows a vector AB.