Using the transformation law for vectors, prove that for any two vectors Ā, B, the inner product of the vectors does not change under the effect of rotation.

Q: Define the cross product (vector product) of two vectors. Which algebraic laws are satisfied by…

A: Cross product of vectors a and b is vector c which is perpendicular to both and b , with direction…

Q: Find a vector v with initial point vector in the direction of v. Enter your answers in i, j, k…

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

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Q: Write expressions for the scalar and vector projections of vector b Illustrate with diagrams?

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Q: Find the length of the vector. v = (0, 2) ||v| = %3D

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Q: Calculating orthogonal projections For the given vectors u and v, calculate projvu and scalvu. u = ⟨…

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Q: Find the projection of vector ū = -i+ 5j + 3k onto the vector i = -i +j- 3k? %3D

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Q: Find the scalar and vector projections of b onto a. a=, b=

A: Given: a=<-5, 12> b=<4, 6>

Q: 1. Find the vector component of the vector ū (-3, 6, 2). [28, 63, 0] in the direction of = %3D

A: We have to find vector component of u =[28, 63,0]  along the direction v=[-3, 6,2] Vector component…

Q: Find the scalar and vector projection of the vector b = onto the vector a =

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Q: 3. Find the projection of u = (2,1,2) onto v = (0,3,4) and the vector component of u orthogonal to…

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Q: {(0, 1,-1), (1,2, ).( 3,-1,4)}

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Q: Give an example to show that vectors are not commutative under the cross product operation. Justify…

A: The objective of the question is checking the commutative fail in vector cross product.

Q: Sketch a graph of u, v, and u + v using the vectors u and v. u = (4, 3), v = (1, 2)

A: Given thatu→=4i+3jv→=i+2jHenceu→+v→=(4i+3j)+i+2ju→+v→=5i+5j

Q: Find the vector projection of b onto a when b = (4, 3), a = (2, –1). 7 (2. –1) 1. vector proj. - 7…

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Q: Find a unit vector perpendicular to both u = (2,3, –4) and v = (-1,1,–4). %3D

A: The unit vector perpendicular to u and v is given by: w=±(u×v)|u×v|

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: . Value of t such that vectors a=, b=, c= are coplanar.

A: Value of t such that vectors a=<1, 1, 1>, b=<2, -4, 0>, c=<1, t, 3> are coplanar.

Q: How do you find out the projection of a vector u on a vector w

A: Projection of vector u on w is nothing but the dot product of u and w divided by magnitude of vector…

Q: Find a vector ī that is perpendicular to the plane through the points A = (2, 5, 1), B = (5,4, –2),…

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Q: ) Determine whether vectors v,(1,2,1), v2 = (1,0,2) and V3 = (1,1,0) spans the vector space (R³, R ,…

A: Given vectors v1=121, v2=102 and v3=110 We have to determine whether the vectors v1, v2, v3 spans…

Q: R) such that the only vectors common to both are (0,0,1,1) & (1,1,0,0).

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Q: Show that the vectors u1=(1, 1, 1), u2=(1, 2, 3), u3 =(1, 5, 8) span R3

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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: Use polar forms to show that, for z#0, z and z- represent parallel vectors. Find the positive…

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Q: ) Let a = (-7, -4, 7) and b = (10, –9, –8) be vectors. (A) Find the scalar projection of b onto a.…

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Q: Calc 3 Find the scalar and vector projections of b onto a. a = ‹-3, -6, -2›,     b = ‹2, 1, 1›

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Q: For vectors ā = (2,4,-1), b =(-1,3,2), calculate the vector projection of b on ā. %3D

A: Vector projection of b→on a→=(a→.b→)a→Consider  a→.b→=(2×(-1))+(4×3)+((-1)×2)…

Q: Calculating orthogonal projections For the given vectors u and v, calculate projvu and scalvu. u =…

A: u=10, 5 & v=2, 6 Now, u·v=102+56=20+30=50 & v=22+62=40=210

Q: Make LU Factorization. b. 2 -4 6 -9 -1 -4 4 -2 7 -3 8 Determine the colump vectors of (h) are…

A: Given matrix is A=14-1537-29-2-31-4-16-17

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

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Q: Calculate parallel component of vector a = [1,2.2] in the directoin of vector v = [7,7,7]. (a1)x¬|…

A: The given vectors area=1,2,2 and v=7,7,7Find the parallel component of vector a.i a∥xii a∥yiii a∥z

Q: Describe the span ot the two vectors (1,0,9) and co. 1,15 geometricellyy in

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Q: Determine the vector projection of the vector (5,0, 7) on the vector (–1,3,4).

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Q: Write a DAG model for computing the dot product between twon-dimensional vectors r and y.

A: Let,  x→=x1i^+x2j^+x3k^y→=y1i^+y2j^+y3k^

Q: QUICK CHECK 6 Verify that the vector (is. 15) has length 1. <

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Q: Let u = (-3, -1, 3) and : = (3, 1, 2). Find the vector component of u orthogonal to a. a 3D

A: Since you have asked multiple questions in single request  so we  will be answering only first…

Q: Find the values of x such that the vectors and are orthogonal

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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: a = the red vector b = the blue vector c = the green vector %3D %3D %3D How would you 'build' the…

A: If you like the solution then please give it a thumbs up... The Answer is:   Equation :…

Q: Find both the scalar projection and the vector projection of b onto a, where a = (3, -3, 1) and b =…

A: Consider the given vector: a=3,-3,1b=2,4,-1 Here, the objective is to find the scalar projection and…

Q: The vertices of a triangle in space are (x1, y1, z1), (x2, y2, z2), and (x3, y3, z3). Explain how to…

A: Given:

Q: Find a parametric representation for the plane that passes through the point (2, –3, 4) and contains…

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Q: Find the length of the vector. v = (5, 0, 3, -2) %3D ||v|| = %3D

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Q: Find the scalar and vector projections of b onto a. a = {1,4} b = {2,3}

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Q: (c) Are the vectors v1 = (3,1,2, 1), i2 = (-1,0,1,0), iz = (3,0,0,3), T4 = (5, –2,0, 4) linearly…

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Q: Find the scalar and vector projection of the vector b = (0,-3,3) onto the vector a = (5,-5,0)

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Q: Check that the vectors U=(0,1,1), v=(3,4,1) and w=(6,2,1) are LD or LI

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Q: 2. Do vectors and form a basis for R’? Explain. 3

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