the functions below. F(x, y, z) = x i – zj+ y k r(t) = 5t i + 9t j – t² k (a) Evaluate the line integral F. dr, where C is given by r(t), –1 s t s 1.

Q: . Use the I function to do the following: (a) find the value of SVxe*dx ,

A: We shall solve first question only as per the answering guidelines.if you want other question to be…

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A: which of the following equations determines E(XY)?

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A: To find the direction in which the function is increasing most rapidly.

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Q: Evaluate the line integral of f(x,y) along the curve C. f(x, y) = x2 + y2, C: y = 2x + 2,0 ≤x≤ 3 8…

A: As per our guideline, we are supposed to solve only one question. Kindly repost other questions as…

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Q: Find div F and curl F if F(x, y, z) = xz°i+ 2y'x²j+ 2z²yk. %3D div F= curl F=

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A: According to the given information, consider the given function.

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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.