4. Find the scalar and vector projections of b onto a (a) a =< 2, 3 >, b =< 4,1> (b) a =<3, -1 >, 6=< 2, 3 >

Q: Determine if the list ( [111], [121], [011], [122] ) of vectors from vector space V = R^3 is…

A:

Q: Let v1, v2, v3 be the vectors in R^3 defined by: v1=[0 5 8], v2=[12,-20,5], v3=[-12,15,-13] a). Is…

A: Solution: (a) We see,            v1 + v2 = [0 5 8] + [12 -20 5]                          = [0+12…

Q: Let a = (6, −3, −5) and b = (7, -2, 10) be vectors. (A) Find the scalar projection of b onto a.…

A: Let  be vectors.(A) To find the scalar projection of .(B) To decompose the vector  into a component…

Q: Q1) Find the equation of the plane passing through the point (4,-1,-5) and perpendicular to the…

A: We have to find the equation of the plane passing through the point (4,-1,-5) and perpendicular to…

Q: Show that the vectors 2 -2 2 uj = 2 uz = 3 uz = 7 1 -5 -3 are linearly dependent. Find all r1, x2,…

A:

Q: Which vector equation below represents the line in R³ that passes through the point (-4, 5, 7) and…

A:

Q: Construct a vector that is perpendicular to the plane containing (−2, 4, 1),(3, 3, -1) and (1, 0,…

A: Construct a vector that is perpendicular to the plane containing (-2,4,1),(3,3,-1) and (1,0,2)

Q: Determine which set of vectors is linearly dependent (a) (b) , (c) (d) (e) (f) O (a) O (b) O (c) O…

A: Recall:A set of vectors is said to be linearly dependent if the determinant is zero.If the…

Q: Which of the following sets of vectors spans R^2?  A. {(1, 1), (–2, –2)} B. {(1, 1), (1, 2)} C.…

A:

Q: Write down the vector equation of the line that passes through the points (x,y,z) = (2,3,7) and…

A: The given problem is to find the vector equation of line that passes through the given two points.

Q: What helps to set of vectors linearly independent?

A: