4. Find the divergence of U = e*Yax + sin(xy) ay + cos²(xz) a,. А. уе*У + х сos(ху) + 2х сos(xz) В. хехУ + у сos(ху) + 2х сos(xz) C. ye*y + x cos(xy) + 2x cos(xz) sin(xz) D. xe*y + y cos(xy) + 2x cos(xz) sin(xz)

Q: Find the scalar product a•b when (i) a= x+2y -z and b=2x+3y +z (ii) a=x-3y +z and b=2x+y +z

A: We have to find the scalar product a·b when (i). a=x+2y-z and b=2x+3y+z(ii). a=x-3y+z and b=2x+y+z

Q: 7. Use matrices to stretch the vector horizontally by a factor of 3.

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Q: Linear Algebra  find a representative of x (vector)

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Q: X, X2 X3 [1 0 LO 1 6 [3 8 -4J

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Q: B = = v= -6 3 6 109 1 -37 -20 -2 -2 -2 1 2 is an orthogonal basis of Rª. Find [v] Fo

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Q: Vector Transformations with Matrices

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Q: n (c) Find a vector b in R³ such that the solution set of Ax = b is a line in R³ parallel to the…

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Q: 8. Use matrices to compress the vector vertically by a factor of X-ахis. and reflect it over the

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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.