Goals: Understand vector algebra. Exercise write out vectors given geometrically
ID: 1347725 • Letter: G
Question
Goals: Understand vector algebra. Exercise write out vectors given geometrically in the math form. Exercise the product of two vectors. Vector: Chapter 3 Problem 74 Vector a lies in the yz plane 63.0degree from the positive direction of the y axis, has a positive z component, and has magnitude 3.20 units. Vector b lies in the xz plane 48.0degree from the positive direction of the x axis, has a positive z component, and has magnitude 1.40 units. Find a in the unit vector notation. From the given information. a = 3.20(0, cos 63.0degree, sin 63.0degree) = (0,1.45,2.85) Find b in the unit vector notation. Find a . b. Find the angle between a and b. Find a Times b.Explanation / Answer
(a)
a = 0i + 3.2*cos63 j + 3.2*sin63 k = 0 i + 1.45 j + 2.85 k <<----answer
(2)
b = 1.4*cos48 i + 0j + 1.4*sin48 k = 0.94 i + 0j + 1.04 k <<----answer
3)
a . b = ( 0 i + 1.45 j + 2.85 k) . ( 0.94 i + 0j + 1.04 k)
a . b = 2.85*1.04 = 2.96 <<----answer
(4)
a.b = lal*lbl*costheta
lal = sqrt(1.45^2+2.85^2) = 3.20
lbl = sqrt(0.94^2+1.04^2) = 1.40
2.96 = 3.2*1.4*costheta
theta = 48.7 <<----answer
(5)
i j k
a x b = 0 1.45 2.85
0.94 0 1.04
a x b = i(1.45*1.04 - 0) - j(0-0.94*2.85) + k(0 - 0.94*1.45)
a x b = 1.51 i + 2.68 j - 1.36 k <<----answer
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