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Assignment 3

# Assignment 3 - skew before starting the rest of the work v...

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Math 222 Assignment 3 1. Recall that sin - 1 x = R x 0 dt 1 - t 2 . Use the binomial theorem and this integral to ﬁnd the Maclaurin expansion of sin - 1 x . 2. Find a unit vector perpendicular to both v = - 3 i + j + 2 k and - i + 2 j + 3 k . 3. Show that the points P ( - 2 , 1 , 3) , Q (2 , 3 , 0) and R ( - 6 , - 1 , 6) are collinear. 4. The vector u makes angles α , β , γ with respectively the X –axis, the Y –axis and the Z –axis. Find γ if α = 2 π 3 and β = π 4 . 5. Show that the angle between the vector joining ( a,b,c ) and ( b,c,a ) and the vector joining ( a,b,c ) to ( c,a,b ) is equal to π 3 . 6. Find the distance between the skew lines (show that they are indeed
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Unformatted text preview: skew before starting the rest of the work): v ( t ) = 7 t 2 + t 4-3 t and w ( s ) = 3-s 5 6 + 2 s 7. Determine the vector parametric equation of the line through the origin and the intersection of the lines (ﬁnd the co-ordinates of this intersec-tion as well) v ( t ) = 2 t + 3-4 t t-3 and w ( s ) = 10 s + 3 5 s-25 4-2 s...
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