Let u = (2, -3, 4) and v = (-2, 1,3). What is the projection of u onto v (proj v u) and the scalar of u onto v (scalv u)? What is the cross product u x v? What is the area of a parllelogram that has two adjacent sides u and v

Q: Let a = (-3, –4, –4) and b = (2, 2, 4) . Find scalars s and t so that sa + tb = (20, 4, 32) %3D %3D

A: We have to find the values of scalers s and t for a=-3,-4,-4 and b=2,2,4.

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: 23. Are the vectors u = and v = orthogonal? Explain.

A: Two vectors are orthogonal, if their dot product is equal to zero.  The formula to calculate dot…

Q: Use the cross product to determine the angle between the vectors [4, 5, 2] and= [-2, 6, 1]. Verify 9…

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Q: Show that v, = (1,0,–1) , v, = (1,0,1) , v3 = (1,1,1) span R’. %3D Express vector v= (4,2, 2) as…

A: Thanks for the question :)And your upvote will be really appreciable ;)

Q: Find the projection of u = onto v = .

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Q: Find the area of a parallelogram formed by the vectors PQ and PR, where P = (6, 6, 0), Q = (3, - 5,…

A: Let the parallelogram be PQRS, whose 3 vertices are P(6,6,0), Q(3,-5,6) & R(3,1,4). Then, these…

Q: (a) Find the vector projection of a onto b , that is, find proj, a . (b) Find a vector in the…

A: We can solve the problem problem using concept of vector.

Q: Show that the dot product distributes over vector addition. Statement: Let ū, i, w be vectors in R".…

A: We will use the distributive law for real numbers which states that  For any real numbers a,b and c…

Q: Use properties of the cross product to find the area of the parallelogra nerated by the two vectors…

A: Recall: Area of the parallelogram form by two vector a and b is a×b

Q: Find the projection of u onto v if u= (5,-3), v = (-1,4).

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Q: Find the cross and v= product uxv² where û =8i +25 - 2k (-3,-1,8)

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Q: If ï = (, 2), find a vector i that is perpendicular to ū.

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Q: Show that VI = (1,0,1) , v, = (1,1,0) , v3 = (1,1,1) span R'. Express vector v= (2, 1, 3) as linear…

A: v1 ,v2 ,v3 ,...,vn span R^n if det(v1,v2,...,vn) is non zero

Q: Let u =[3, -1] and v = [0, 1] can you find the vector[h, k] that is not in Span{u,v}? either give an…

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Q: If u • vx w or v • or w • v equal to zero, then the vectors u, v , and w are coplanar... True False

A: Concept Used: Three vectors are said to coplanar if their scalar triple product is zero That is  [u→…