1. Find ar, aN, N, T, and k for: (a) F(t) = (5t, t, 4t) at the point (10, 4, 8) (b) ř(t) = (1 – 2t², 2 – t², t³) at the point (-1,1, –1) (c) r(t) = (5t, 3 cos 4t, 3 sin 4t)

Q: Match each graph with its equation. v F(t) = (cos(t), sin(t), t) ]F(t) = (t, sin(t), 2) F4) – (1, 2,…

A: The first vector function is rt=cos t, sin t, t. The components are x=cos t, y=sin t and z=t. Square…

Q: 5. Find the values of a and b such that dx tan 1 + sinx a + b . %3D

A: We need to integrate ∫11+sinxdx

Q: O For y = Asin (x- C)] + D Identify with graph A. B, C and D for the sin function y = -2sin (;x -) +…

A:

Q: If (x, y) = (-3, –3), then find the corresponding values of r > 0 and 0 < 0 < 2n in radians.

A: Explanation of the answer is as follows

Q: 1) State whether the following functions are odd, even or neither: a) t³ sin(wt) b) t cos(2t) c)…

A: Since you have posted a question with multiple sub parts, we will provide the solution only to the…

Q: (b) c = 9 · t + sin ( 2 - t² – 2 . t3) .2-2.8) (b) c 9 t+ sin ( 2 The answer is

A:

Q: /4 (6) Evaluate I cos y dz dr dy = A. B. C. D. A

A:

Q: Compute cos æ dæ. cos x +C 3 cos a sin x +C sin r cos a + cos x +C sin a +C 3 sin r + sin I 3 sin a…

A: Given, ∫cos3x dx We can write it as by using the trigonometric identity as, cos2x=1-sin2x∫cos3x…

Q: 11.Show that A cos (ω0t) + B sin (ω0t) can be written in the form r sin(ω0t − θ). Determine r and θ…

A:

Q: 2. Show that: (i) sin (ii) A" cos (a + bx) = [2 sin bx + n cos - sin b (iii) A cot (a + br) = sin (a…

A:

Q: Find z where z = sin (æ²) cos (4²) COS

A: The given function is z=sinx2 cosy2.

Q: Find C if r(t) = ⟨et, 3 cos t, t + 10⟩ + C and r(0) = ⟨0, 0, 0⟩.

A: We have given function r(t)   r(t) = ⟨et, 3 cos t, t+10⟩ +C   We have to find the value of C   It…

Q: 1. If x-y? = 25, then y" = %3D a.) b.) c.) - d.) - 2. If y = cos(3x+1), find y' a.) 3 sin(3x+1) b.)…

A: Given:   (1) x2 - y2 = 25    (2) y = cos(3x+1)

Vector Arithmetic

Vectors are those objects which have a magnitude along with the direction. In vector arithmetic, we will see how arithmetic operators like addition and multiplication are used on any two vectors. Arithmetic in basic means dealing with numbers. Here, magnitude means the length or the size of an object. The notation used is the arrow over the head of the vector indicating its direction.

Vector Calculus

Vector calculus is an important branch of mathematics and it relates two important branches of mathematics namely vector and calculus.