Let S be the parallelogram determined by the vectors b, 8. and b2 = 2 Compute the area of the image of S under the mapping x-Ax. and let A = 3D - 4 1 1 The area of the image of S under the mapping XHAX is (Type an integer or a decimal.)

Q: Graph and find the area of the parallelogram formed by the vectors u = and v = .

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Q: Consider A = ⟨0, 4, 2⟩, B = ⟨6, −1, 0⟩ and C = ⟨3, 0, 1⟩. draw the vectors A, B, and C in…

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Q: Compute the orthogonal projection of v= 7 onto the line through 4 2 and the origin.

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Q: Let a = (- 6, 3) and b = (1, – 4). Compute the dot product.

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Q: Suppose that the vectors [1, –3, 1] and [2, 4, –1] form the sides of a parallelogram. Find the…

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Q: if vector AB=i+7j-4k and B is the point (9,3,5) find A

A: Let A=ai^+bj^+ck^B=di^+ej^+fk^ be twovectors.Then AB→=d-ai^+e-bj^+l-ck^

Q: 4. Subtract the vectors shown. (blue - green)

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Q: Find the cross product a × b. a = (6, 5, -4), b =(2, -1, 1) Verify that it is orthogonal to both a…

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Q: Describe the Z-axis in R as the span of a vector. Can you describe it as the span of other vectors…

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Q: 7. Show that the vectors A=4a, -2a + 2a, and B = -6ā, +3ā, -3ā. e parallel to each are other.

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Q: Find the equation of the plane sanned by the above two vectors

A: Given: Two vectors u=223 and v=-20-3. To find: Equation of plane spanned by given vectors.

Q: For the matrix N = Answer: 9 22 4 3 7 1 4 11 3 etry this question below find three different…

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Q: ? (2,3), (0,0) }

A: Let S=2, 3, 0, 0. We need to find whether the set S spans a line or all of ℝ2.

Q: Determine if u = (4,3) and v = (1/2 , - 2/3) are orthogonal, parallel or neither.

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Q: Find two vectors v1 and v2 whose sum is , the rest is on the photo

A: We know if two vectors are parallel then they have same direction or opposite direction. If two…

Q: Find the area of the parallelogram spanned by the vectors -i+ 2j and i - j.

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Q: t a = (3,3) and b = (4,1) draw and label the vectors a, b, -a and b - a on a set of coordinate axes.

A: Given vectors a=(3, 4) and b=(4, 1)

Q: Determine if u = (0,3, -4) and v = (1, -8, -6) are orthogonal, parallel or neither.

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Q: Let X and Y be points in R³. Let P be a point on the line segment joining X and Y such that the…

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Q: Sketch the vectors = (2, 3,-6) and w = (-1,1,1) and draw -U, v + w and 7 - w.

A: The given vectors are

Q: 3. If a = 3x - 5y and b=-2x+9y, write the vector 5a-8b in terms of x and y

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Q: Determine the vector 2a – b if a = -4i + 5j and b = 7i + 2j. %3D

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Q: Let S be the parallelogram determined by the vectors b. image of S under the mapping x++Ax. and b₂…

A: Given b1=-24, b2=-27 and A=2-7-57. Compute the area of the image of S under the mapping x→Ax.

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.