Question

Part A Given two vectors A 4.80 i + 7.40 3 and B :-550 İ 2.60 J , find the scalar product of the two vectors A and B. A B- Submit Previous Answers Request Answer X Incorrect; Try Again; 5 attempts remaining Part B

part A&B please

Answer 1

A middot B = (A_x x + A_y y + A_z z) middot (B_x x + B_y y + B_z z) = A_x B_x x mid x + A_x B_y x middot y + A_x B_z x middot z + A_y B_x y middot x + A_y B_y y middot y + A_y B_z y middot z + A_z B_x z middot x + A_z B_y z middot y + A_z B_z z middot z with the values given by Eq. (24), this reduces to A middot B = A_x B_x + A_y B_y + A_z B_z This picture tells how to calculate the scalar product between two vectors if they are expressed in component form or in terms of unit vectors.. Vector A is expressed addition of 3 components i.e. x, y, z components of A . Similarly B is also expressed. In the next step the multiplication is carried out of each terms. The last step uses the following logics

This picture tells how to calculate the scalar product between two vectors if they are expressed in component form or in terms of unit vectors.. Vector A is expressed addition of 3 componets i.e. x,y,z components of A . Similarly B is also expressed.

In the next step the multiplication is carried out of each terms.The last step uses the following logics

dot product between unit vector x and x, y and y, z and z unit vectors are 1 as they are unit vectors and they have 0 angle between them.If you remember the formula for dot products of two vectros in term of magnitude and cosine of angles

these dot product reduces to

x^{^} . x^{^} = I x^{^} I I x^{^} I cos(0) = 1 * 1 * 1 = 1

But the dot product of x with y and z will be zero as they are orthogonal vectors and dot product between them contains a cosine term which become zero for orthogonal vectors i.e cos(90) = 0. Similar reasoning for dot product between y and z, y and x, z and x, z and y.

if you focus on the picture, in the end it tells that the dot product essentially reduces to multiplications of respective components i.e x component of A multiplied with x component of B + y component of A multiplied with y component of B + z component of A multiplied with z component of B

Vector A has x component 4.8 and B has 5.5. Vector A has y component 7.4 and B has -2.6. They don't have z components.

so for our case A.B = 4.8 * 5.5 + 7.4 * (-2.6) = 7.16