A vector = 4.2 x - 5.3 y, and B vector = + 3.4y. C vector = A vector + B vector

Question

A vector = 4.2 x - 5.3 y, and B vector = + 3.4y. C vector = A vector + B vector = We have two points. Point 1 is (2, 6) and point 2 is (3, 4) raw r_12 Express r12. Express |r| Note that r_12 = |r_12|r cap 12 where r_12 is the unit vector. What is r_12? The magnitude of a vector E vector is |E| = 20.0. Its angle from the x-axis is alpha = 30 degree in the negative direction. What are the values of E_x and E_y? Draw E_x and E_y..R_x = 4.3, R_y = -2.1 What is R vector ? What is the angle of R_vector from the x-axis? What is R_cap ? Draw R vector.

Explanation / Answer

a) C = 4.2 x -1.9 y

b) r12 = ( 3-2)i + (4-6) j = i - 2j

magnitude of R = sqroot ( 1^2 + 2^2) = sqroot (5)

unit vector = i /sqroot 5 - 2j/ sqroot 5

c) Ex = -20 cos 30 = 17.32 i

Ey = 20 sin 30 = 10 j

d) R = Rx + Ry = 4.3 i -2.1 j

Magnitude of R = sqroot ( 4.3^2 + 2.1^2) = 4.785

unit vector r = 4.3 i/ 4.785 - 2.1 j/ 4.785

angle = tan^ -1*( -2.1/ 4.3) = 26.029 from the x axis

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