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

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

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Q: express the vector (4,5,5) as a linear combinations of vector (1,2,3) (-1,1,4) and (3,3,2)

A:

Q: Find the sum of the vectors (–1,4) and (6, –2) and illustrate geometrically.

A: A vector V→=a,b can be represented on the cartesian plane, From the vector law of addition,…

Q: Find the dot product of the pair of vectors (-2, 5) and (4, 1).

A: Given : < -2 , 5 > and < 4 , 1 >

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 vector with length 3 making an angle of 7π/4 with the positive x-axis.

A: Given that the vector with length of 3 makes an angle of 7π/4 with the positive x-axis.

Q: If a vector is multiplied by a positive scalar, how is the result re-lated to the original vector?…

A: Explanation:

Q: Find two vectors v1 and v2 whose sum is ⟨−3,5⟩, where v1 is parallel to ⟨1,−1⟩ while v2 is…

A: Given Data: The sum of vector v1 and v2 is <-3,5>. The vector v1 is parallel to the vector…

Q: Find two unit vectors parallel to (2, 3).

A:

Q: Find two vectors v1 and v2 whose sum is ⟨−5,0⟩, where v1 is parallel to ⟨5,1⟩ while v2 is…

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Q: Find the volume of the parallelepiped determined by the vectors a = (3, 4, – 1), b = (0, 4, 2), с 3…

A: Given the vectors, a→=3,4,-1b→=0,4,2c→=2,5,1

Q: Find two unit vectors orthogonal to both (2, 6, 1) and (-1, 1, 0)

A: The given vectors are The unit vectors can be obtained by the formula Now, find the cross product…

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

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

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Q: Find a vector that has the same direction as [4, 2,5] but has length 35.

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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: See this solution in below

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: Give a vector of length 13 that is parallel to (-1,2, –2).

A: Topic- vector calculus

Q: Find two unit vectors orthogonal to both (1,-1,1) and (1,0,3)

A:

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

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Q: Find a vector that has the same direction as (-4, 6, 4) but has length 6.

A: we have to find a vector that the same direction as <-4, 6, 4> but has length 6

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 area of triangle with the vectors p(0,1,4),0(-5,9,2) and R(7,2,8)

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Q: Find two vectors that are orthogonal to ⟨0, 1, 1⟩ and to each other.

A: Vector: Let the two vectors are v and w. We have to find the two vectors which are orthogonal to…

Q: Find the measure of the angle between the two vectors. (-4, 5) (-6,3) ►

A: Consider the graph

Q: Determine the volume of the parallelepiped formed by the vectors P = (2,4,3), Q = (1,3,2) and R=…

A:

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

A: We can find the unit vector as below.

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

A:

Q: 7. Find a vector that has the same direction as (-2,1, 2) but twice the length.

A: GIVEN DATA : Vector of direction -2, 1, 2       TO FIND : The vector of the same direction but twice…

Q: Find the vector that has the same direction as (2, 6, -9) but has length 4.

A:

Q: Determine the area of the parallelogram determined by the vectors ⟨5, 3 ⟩ and ⟨−8, −1 ⟩. Determine…

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Q: Find two unit vectors orthogonal to both (6, 9, 1) and (-1, 1, 0). (vector with the smaller…

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Q: Express the vector (2, –5, 3) in R³ as a lincar combination of the vectors (1.-3, 2), (2, –4, -1)…

A:

Q: Find two unit vectors orthogonal to both (2, 3, 1) and (-1, 1, 0).

A: Unit Vectors orthogonal to vectors  <2,3,1> and <-1,1,0>…

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 magnitude of the projection of (- 1, 2) onto the vector (3, 5)

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Q: find two unit vectors orthogonal to (5,-5,3) and (-3,5,2)

A:

Q: Find two vectors v1 and vz whose sum is (-4, –4, 5), where vj is parallel to (1, 1, –2) while v2 is…

A: we have to find the two vectors v1→ and v2→ whose sum is -4,-4,5 where v1→ is parallel to 1,1,-2…

Q: Find a vector which is orthogonal to the vectors ū = (2, –2, 1) and ū = (4, 3, – 1).

A: Explanation of the answer is as follows

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

A: See the attachment

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: Determine the angle between the vectors a = (4, 5, 2) and b = (-3, 6, 0)

A:

Q: Find a vector a that has the same direction as (-8, 9,8) but has length 3.

A: The solution is given below

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)

A:

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…