t) = (et, e24), to = 0 لاخت لا rve represented by the vector-valued function, and sketch the vectors r(t) and r'(to). (0, 1) 3 -1 r (1, 0). 2 (1, 1)

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: Find terminal point Q of vector PQ =    <9, −2, 1>   with the initial point at…

A:

Q: Find 3-dimensional vectors V₁, V₂, V, satisfying V₁V₁ = 4, ₁₂ = -2, V₁ V₂ = 6, V₂ V₂ = 2₁ V₂ V₂ =…

A:

Q: Suppose f(x, y) = (a) ▼ f(x, y) = (b) ▼ f(-0.7, 7) = tan(x) + y and u is the unit vector in the…

A: Given that f(x,y)=tan(x)+y  and u is the unit vector in the direction of <2,3>now, ∇f(x,y)=fx,…

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

A:

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: Suppose ₁, 2 are vectors in R². Is to inatifu your cor [8] in Span({₁, ₂})? Explain your reasoning…

A:

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 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 a unit vector orthogonal to both u and v. u = 2i5j + 3k 2-3 V = + -k 10

A:

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: ū = (-/3, –1) and w = (1, /3) E. |

A:

Q: What is the terminal point of the vector a = (4, 1) based at P = (1, 5)? Answer:

A: Use the definition of terminal point, we solve this problem as in next step.

Q: Find the vector equation for the line of intersection of the planes x + y - 4z = 4 and + 4z = -2

A: We have to find the vector equation.

Q: 123. If F is a vector point function and a is a constant vector then show that i) V (a · F) = (a-V)…

A:

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

A:

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: If ï = (, 2), find a vector i that is perpendicular to ū.

A:

Q: 6) Find two unit vectors that are parallel to the tangent line of f(x) = tan(x) at the point (7,0).

A: Given that f(x)=tanx We have to find two unit vectors that are parallel to the tangent line f(x) at…

Q: The vector F = −ar + 2a expressed in RCS and in terms of pis

A: We have to expressed the vector F→=-ar+2aθ in RCS in terms of ϕ.

Q: 11) For u = (2,3,-1) and v (-1,01) find; %3D II a) proj,(u) b) The vector component of u orthogonal…

A: For finding projection using the formula, projv(u)=v→.u→v→2v→ The vector component of u orthogonal…