a linear combination of the vectors Can we express the vector a = (2, – 5, 3) as e = (1, 1, 1), ez = (1, 2, 3) and e, = (2, – 1, 1) in R'(R).

Q: 13. Find a vector equation of the line through (2, 1) parallel to (x, y) = (-2,7)+t(3,5). 14. Find a…

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Q: Let B be a subset of R4. Which of the following statements are correct? If |B| = 5, then B spans R4…

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Q: Qe A) Find the vector 5 unit length in the direction of vector perpendicular to the iHane which…

A: We have to find the perpendicular vector first.

Q: 1. y -2+ 2.

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Q: Find a unit vector perpen dicular to the plane of the vectors a = (2, -3,1) and b = (1, 2, -4)

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Q: For what value of m, the vector (m,3,1) a  linear combination of e\index{1}=(3,2,1) and…

A: We have to find the value of 'm' such that  is a linear combination of Assume

Q: Suppose f(x,y) = = tan(x) + y and u is the unit vector in the direction of (-3,-1). Then, a) ▼ f(x,…

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Q: Find F‘(0)  for the function f(x)=3xe5x b) Given vectors a=(1,3,-2) and b=(1,1,2) , find  3a +2b…

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Q: Find two unit vectors orthogonal to a = (-5, -1, 1) and b = (-1,2,3) Enter your answer so that the…

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Q: = 2. Are the vectors V = (2, — 4, 1) and w Show work and briefly explain. (3, 2, 2) orthogonal? 3.…

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Q: The finishing times, in minutes, for running marathons have an unknown distribution with mean 297…

A: Mean = 297 Standard deviation = 32 Sample size = 41

Q: For the vectors A=x + 2ŷ – î = (1, 2, – 1), B=ŷ + î = (0, 1, 1), C=î-ŷ = (0, 1, 1), a) Prove that Ax…

A: Correct last vector coordinates representation

Q: You are looking down at a map. A vector u with |u| = 1 points north and a vector v with |v|= 7…

A: None option is correct. The details solution of the given question is given below in step 2.

Q: Find the velocity vector v(t), given the acceleration vector a(t) = (3e¹, (Use symbolic notation and…

A: Formula for the acceleration is We have and the initial velocity

Q: Q2/ (a) Let A (2,3,0) and B (-1,- 2,- 4) be two points. Find the vector AB in terms of the standard…

A: The detailed solution is as follows below:

Q: Find the magnitude of the vector AB A=(4, 1) and B=(-3,0)

A: Given that, A = (4, 1) B = (-3, 0) We have to find the magnitude of the vector AB.

Q: (14) The straight line L passes through the origin O and is in the direction i+mj. The straight line…

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Q: Find a vector parametrization of the line through P = (3, -5, 7) in the direction v = (3, 0, 1)

A: Given:P=3,-5,7v=3,0,1

Q: Find a vector x = ( c, d) that has dot products x · r = 1 and x · s = 0 with two given vectors r =…

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Q: Vectors a' and b are perpendicular to one another. Find k : a'(k², –k, 1), b´ (k, 3, – 2)

A: Scalar product of two vectors

Q: Consider A = (0, 4, 2), B = (6, -1, 0) and C = (3, 0, 1). (i) Find the unit vector having the same…

A: We have to find the unit vector having the same direction as B-2A+12C Then, we can proceed further.

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: In R, evaluate the alternating 2-form 5 = -3· dx A dy on the pair of vectors (a, b) if a = (4, 2,…

A: Given that, ξ=-3.dx∧dy on (a,b) Where a=(4,2,12),b=(-7,-4,8) The objective is to show that ξ(a,b).

Q: Find the magnitude of the vector AB A=(-2,1) and B=(4, 9

A: Given: