Consider the following vectors u = (-1, 1, 2), v = (3, 6,-1) and w = (0, 1,-4). Find %3| i. The distance between u and v ii. v.w (dot product) iii. The angle between w and u iv. The vector perpendicular to u and v Find the arc length of the curve y = log(1/cosx) from x = (T/4) to x = - (π/ )

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A: Given, (A) rt = cost, sint  we have to find  r'π4  (B) rt = t2, t3  We have to find r'4

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A: The parabola y = x2 and the point (6, 36)

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A: Explained below

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A: Given y'→=Ay→ Here A=1245 We have to find right hand side vector F→(t,y)→.

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A: Vector equation of line

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A: Given that r→t=32t,e3t,e-3t. Find the value of r→'t and r'→'t.…

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Q: 3. if the position function vector r = ti +6tj , find the direction of the vector at time 1 sec جد…

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A: This question can be solved using the concept of vectors and derivatives.

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A: Given, r(t)=2 cost i+2 sint j+t k

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A: Part A,             rt=cos5t,sin5tTo find : r'π4

Q: Q1: For the position vector r = et cos(t) i+ et sin(t) j+ e¯tk, find the velocity and acceleration…

A: Note : There are many questions in the above image. So I will answer the first question and…

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A: First we find unit tangent vector any arbitrary point on given curve

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A: r( t ) = 3 sin t  i→+ 4 cos t  j→r( t0 ) = 3…

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Q: Given r→(t)=⟨cos⁡2t,−sin2t,4t⟩, find the unit tangent vector

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