A PARTICLE MOVES WITH A SPEED OF 2 m/s IN THE DIRECTION OF THE VECTOR a=(5,-3,2) determine the x, y, and z components of the velocity vector

Q: Determine a vector equation for hte line through the point: (-2, 0, -8) perpendicular ot the plane:…

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Q: Find parametric equations for the line whose vector equation is given. (a) (x, y) = (4, –6) + t(1,…

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

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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: The vector describing a particular particle is given by F (t) = Rcos (wt) î + R sin (wt) ĵ, where R…

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Q: Find the distance from the origin to the plane through the point (-6,3, -2) and having 5i - 3j° + 4k…

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Q: Find the sine of the angle between vectors u = (-3, 2,6) and v = (3,2,6) by using the cross-product.

A: Given: The vectors u =(-3, 2, 6) and v=(3,2,6) Find : The sine of the angle between the vectors u…

Q: Find both the vector equation and the parametric equations of the line through (0,0,0) that is…

A: Given vectors area. u=2,0,2w=-2,-1,0a=0,0,0 Find the vector equation of the line perpendicular to u…

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: Find an equation for the plane that passes through the point (3, -2, 1) normal to the vector n = 2i…

A: Given:A point (3, -2, 1) normal to the vector n = 2i + j + kThe normal vector can be written as,

Q: Find the scalar equation for each line: (a) a line through the point (-6, 7) with direction vector…

A: Since you have asked multiple question, we will solve the first question for you as per our guide…

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 normal to the plane -2x - 3y = 12 - 4z.

A: Given  a vector -2x-y=12-4z. We need to find the vector normal to the plane.

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: 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).