1) compute || w|| 2) use || w|| to define a unit vector u, which is parallel to w

Q: 18) a) Find a unit vector that is orthogonal to both u = and v = . b) find the area of the…

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Q: 2. Let x = (1, 1, 1, 1)" and y = (8, 2, 2, 0)". (a) Determine the angle 0 between x and y. (b) Find…

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Q: 5. a) What is the orthogonal projection ŷ, of y = 1 = ( ² ) U = and the origin? -3 9 onto the line…

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Q: for 2. Given the vector space W given by W = Span Image A Image B Can you write W as a span of fewer…

A: Solution: We clearly see, image B can be formed by stacking two rows of two image A's each.  i.e.,…

Q: 11. Affine Coordinates: Define the basis vectors of a coordinate system that is not orthogonal to…

A: The set of vectors B of a vector space V is called a basis for V if every element in V can be…

Q: (6.) Let u (1,3,-2) and v (0, 2, 2). %3D (а. Determine compyu the scalar projection ofu onto v. (b.…

A: “Since you have posted a question with multiple sub-parts, we will solve first three subparts for…

Q: I L is a line in 2-space or 3-space that passes through the points A an 3, then the distance from a…

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Q: 4.) Correct of K vector representation for of terms B the velatie. positive normal and tangential…

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Q: 3. (a) The component of u along v is the scalar u cos e and can be expressed in terms of the dot…

A: Given (a)  The component of u along v is the scalar |u| cos θFormula: u·v=|u||v|   cos θ

Q: The vector projection of u = [3, -4, -2] on the x-axis is: %3D 3 29 3 29 3í

A: The direction ratios of the X-axis are, (1,0,0) Also, u•(1,0,0) = 3 is the scalar projection on the…

Q: Let y= [ -3 -2 3] and u= [2 1 -1]   A) Find the orthogonal projection of y onto u.   B) Compute the…

A: Given vectors are  .A)

Q: Consider the set of vectors (V1, V2, Vs}: statements is true about the span{V1, V2, V3}? {·E·} O…

A: We need to verify which statement is true for the given vectors:.The solution for the given problem…

Q: Q7. a) Consider the vectors u , v and w are defined by u = i+j ,v = i+ 4j and w = 4i – 3j i. If the…

A: Given :

Q: (a) Give the horizontal and vertical components. (b) Find |v||. (c) Graph v and interpret |v||. 15.…

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Q: The transformation Po[1, ₂] = cos²0 cos sin cos sin sin²0 [1, ₂] onto the line through the origin…

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Q: Let u||y be the projection of u along v. Which of the following is the projection u along the vector…

A: The projection of vector u on vector v equals ucosθ where θ is the angle formed by the two vectors.…

Q: -{{} O Consider the bases B = Find the B-coordinate vector of i= (2, –1).

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Q: If a line is parallel to the vector 6i + 7j+ 2k and passes through the point P= (5, 1,7), then the…

A: Given that a line is parallel to the vector 6i+7j+2k and passes through the point P=5, 1, 7. We know…

Q: Use the vectors u = (1,-3,5) and v=(2,1,-3) to Find a. cos(theta), where theta is the angle between…

A: As we know that; The expression for the dot product between the two vectors u & v is: u·v=uvcosθ…

Q: 1 ··· 7. Compute the orthogonal projection of origin. onto the line through A- 2 and the

A: Let us denote the vector 17 by u. The line through the vector -42 and the origin is spanned by the…

Q: consider the following: u = , v = (a) Find the projection of u onto v. (b) Find the vector…

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Q: A)The mapping f holds in the following equation. = 0 + yz xy dxdy Əydz + xz- Əxdz We put: x = wu, y…

A: we have given xy∂2f∂x∂y+yz∂2f∂y∂z+xz∂2f∂x∂z=0   ...i according to question  we put  x=wu . y=wv ,…

Q: Find the projection of the vector v onto the vector w if v = 2i + j and w = 6i + 3j

A: we have given v and w vectors . We have to find the projection of the vector v onto the vector w

Q: Prove Theorem .Let Q be an orthogonalmatrix. detQ=+-1

A: Given that, “Q” be an orthogonal matrix, So, QQT=I=QTQ…