) Let a = (-7, -4, 7) and b = (10, –9, –8) be vectors. (A) Find the scalar projection of b onto a. Scalar Projection: (B) Decompose the vector b into a component parallel to a and a component orthogonal to a. Parallel component: Orthogonal Component:

Q: Let a = (-10, –10, 10) and b = (8, –4, –4) be vectors. (A) Find the scalar projection of b onto a.…

A:

Q: The orthogonal projection of the vector u=(-1,-2) on a=(-2,3) is 8 12 а) 13 13 13 b) 8 13 12 4 c) 13…

A:

Q: Let u = -i + j, v = 3i - 2j, and w = -5j.Find specified scalar 5u . (3v - 4w)or vector.

A: It is given that  u = -i + j, v = 3i - 2j, and w = -5j

Q: Find the scalar and vector projections of b onto a. a = (-3, -6, 2), b= (3, 2, 1) -꼭 19 compab = 7…

A:

Q: Let a = (-10, – 10, 10) and b = (8, –4, –4) be vectors. %3! (A) Find the scalar projection of b onto…

A: Here find projection of b on a

Q: Let a = (5, 3, 8) and b = (-3, –2,–7) be vectors. (A) Find the scalar projection of b onto a. Scalar…

A: Given data is: a=5,3,8 and b=-3,-2,-7

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: 11) Use properties of vector to determine the value of the dot product å. b for the vectors ở = 21…

A:

Q: Find the scalar and vector projections of b onto a. a = (1, 5), b = (-6, 1) comp,b proj b

A: a = 1i + 5j  b =  -6i + 1j

Q: Find a basis for the plane 3r - y+1z 0. withe the vectors required to be orthogonal to each other.…

A: Let's find.

Q: Let u = -i + j, v = 3i - 2j, and w = -5j.Find specified scalar 4u . (5v - 3w)or vector.

A:

Q: Find the scalar and vector projections of b onto a. a = ⟨-3,4⟩, b = ⟨7,9⟩ scalar projection of b…

A: The given points in vector form, a→=-3i^+4j^b→=7i^+9j^ The Scalar Projection of b onto a, is given…

Q: Let u = 2i - 5j, v = -3i + 7j, and w = -i - 6j. Find the specified vector or scalar v - u.

A:

Q: Consider vectors a = (2, -8), b = (-1, 4), andc = 0. Determine the non-zero scalars a and B such…

A: Consider vectors a=(2,-8) , b=(-1,4) and c=0. We have to determine the non-zero scalars alpha and…

Q: Let u = -i + j, v = 3i - 2j, and w = -5j. Find the specified scalar or vector: 4u.(5v - 3w)

A: Given: u = -i + j, v = 3i - 2j, and w = -5j

Q: Find the projection ( Projee ) of the Vector. à = 2i +3j +3k on the vector %3D b= i-2j +K. %3D

A:

Q: Calculate a projection of vector B on A and prophecy of vector A on B. A = 4i - 3j + 2k.     B = 3i…

A:

Q: Determine the vector, parametric, and Cartesian (Scalar) equations for the line that passes through…

A: To find the equation of line that passes through the point A(4,-1) and is also perpendicular to line…

Q: Find the scalar and vector projections of b onto a. a = (1,6), b = (-7, 1) compab = projb =

A:

Q: Let u = 2i - 5j, v = -3i + 7j, and w = -i - 6j.Find specified vector or scalar -4w.

A: It is given that  u = 2i - 5j, v = -3i + 7j, and w = -i - 6j

Q: Find the scalar and vector projections of b onto a. a = (-3, 4), b = (7, 9) scalar projection of b…

A: Give a→=<-3,4>, b→=<7,9>We find the scalar and vector projection of b→ and a→

Q: Let a (-2, –1,9) and b = (-8, 4, 3) be vectors. (A) Find the scalar projection of » onto a. Scalar…

A:

Q: Find the scalar and vector projections of b onto a. a = 3i - j+ 6k, b = j+k = j+ k compab = projąb =

A: Here we find the scalar and vector projection of b→ onto a→where a→=3i∧-j∧+6k∧ , b→=j∧+12k∧

Q: B) Let V = -2î +j- 5k and W = projection and the vector projection of V onto W. -21 – 4j – 3k be…

A: The given vectors are v→=-2i^+j^-5k^ and w→=-2i^-4j^-3k^

Q: a. Please provide a well explained answer for the follwoing. And explain what are the components of…

A: Components of vector  In two dimensional ,any  vector can divide into two components x -…

Q: Let ri = xji+yij+z¡k, r2 = x2i+ Y2j + z2k and r3 = x3i+ Y3j + z3k be the position vectors of points…

A:

Q: . Prove that there is no distinction between contravariant and covariant vectors if the…

A:

Q: siven the vectors ủ = (-3, 3, 1) and v = (- 1, 1, 2), calculate the vector projection of ū onto v

A:

Q: Find the scalar and vector projections of b onto a, where a = (-1, 1, 2) and b = (-2,7,2). 1. comp,…

A:

Q: Let u = 2i - 5j, v = -3i + 7j, and w = -i - 6j. Find specified vector or scalar||-2u||.

A: given that u=2i-5j v-3i+7j w=-i-6j

Q: Find the scalar and vector projections of b onto a, where a = (-1,1,2) and b = (-4,5,8).

A: The solution of the problem is given in the next step.

Q: Find the scalar and vector projections of b onto a, where a = (1, 2) and b = (-4, 1). 1. comp, b 2.…

A:

Q: Consider the vector y = [1 2 3]. Find the orthogonal projection of y onto the plane x, - 2x2 + 4x3 =…

A: Given vector is y=1,2,3 Given plane is x1-2x2+4x3=0 Normal vector to the p[lane is n=1,-2,4…

Q: Consider the points C(3,-2,0), D(-1,5,-1). Let b be the vector with representation CD. Write b in…

A: Ans:

Q: Consider the four vectors X1 = (0, 0, 0)', X2 = (1, 0, 0)", x3 = (1, 1, 0)", x4 = (1, 0, 1)'. %3D…

A:

Q: Let ri = xi+yıj+z¡k, r2 = x2i+ Y2j + z2k and r3 = x3i+ Y3j + z3k be the position vectors of points…

A:

Q: Let u = 2i - 5j, v = -3i + 7j, and w = -i - 6j.Find specified vector or scalar|| 2u||.

A: It is given that u=2i^-5j^, v=-3i^+7j^, w=-1i^-6j^. We have to find 2u   2u=4i^-10j^…

Q: Let a = (8, -6, 7) and b = (4, –10, 4) be vectors. (A) Find the scalar projection of b onto a.…

A: Givena=8,-6,7b=(4,-10,4,)

Q: The position vectors of A and B with respect to the origin O are a and b respectively. M is the…

A: Given that position vector of A and B with respect to the origin O are a and b respectively. M is…

Q: Find the scalar AND vector projections of a onto b where a=(0,1,-2) and b=(-1,0,3)

A: Given , a = (0,1,-2) and b = (-1,0,3).

Q: Let u = -i + j, v = 3i - 2j, and w = -5j. Find the specified scalar or vector: 5u.(3v - 4w)

A: Given: u=-i+j, v=3i-2j and w=-5j

Q: Let u = 2i - 5j, v = -3i + 7j, and w = -i - 6j.Find specified vector or scalar 3v - 4w.

A: Given  u = 2i - 5j, v = -3i + 7j, and w = -i - 6j. We need to find the specified vector or scalar…

Q: Let v = i - 5j and w = -2i + 7j.Find the specified vector 6v - 3w or scalar.

A: Given: v=i-5j and w=-2i+7j

Q: Let a = (-6, 2, 7) and b = (10, –1,6) be vectors. (A) Find the scalar projection of b onto a. Scalar…

A: Scaler projection of b onto a = b→.a→a→

Q: If A = -ax + 6a, + 5az and B = ax + 2ay + 3ax find: (a ) the scalar projections of A on B, (two…

A:

Q: Find the scalar and vector projections of b onto a, where a = (1,2) and b = (-–9, 1). %3D 1. comp, b…

A: We have to e the magnitudes of thr given vector first.

Q: Let u = 2i - 5j, v = -3i + 7j, and w = -i - 6j. Find the specified vector or scalar l-l-2ul.

A: Here given as u = 2i - 5j, v = -3i + 7j, and w = -i - 6j. Thus -2u=-2·2i+2·5j=-4i+10j