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Calculus Solutions 20 - Answers to Odd-Numbered Problems...

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Answers to Odd-Numbered Problems A-19 11 Parallel if N V = 0; perpendicular if V = multiple of N 13 i + j + k (vector be tween ~oints) is not perpendicular to N; V . N is not zero; plane through first three is x + y + z = 1; x + y - z = 3 succeeds; right side must be zero 1 5 a x + b y + c z = O ; a ( x - x o ) + b ( y - yo)+c(z-zo)=O 17cosB= $,$,* 19 &A has length $ 21 P = $A has length $ 1 ~ 1 23 P = -A has length IAl 25 P = 0 27 Projection on A = (1,2,2) has length g; force down is 4; mass moves in the direction of F 29 IPlmin = & = distance from plane to origin 31 Distances 2 and 2 both reached at ($, $, - $) 6 6 3 3 i + j + k ; t = -$;(!,-5,-;);-& 35 Same N = (2, -2,l); for example Q = (0,0,1); then Q + $N = (2, -$, v) is on second plane; $ 1 ~ 1 = 37 3i + 4j; (3t,4t) is on the line if 3(3t) + 4(4t) = 10 or t = g; P = (g, g), IPI = 2 ~ 9 2 x + 2 ( ~ - f x ) ( - f ) = 0 s o x = ~ = ~ ; 3 x + 4 ~ = 1 0 g i v e s y = ~ 41 Use equations (8) and (9) with N = (a, b) and Q = (xl , yl ) 43 t = A'B B onto A 45 aVL = ?LI - ?LIII; aVF = $LII + $LrII 4 7 V . L I = 2 - l ; V . L I I =-3-l,V.LIII = - 3 - 2 ; t h u s ~ . 2 i = 1 , ~ - ( i - & j ) = - 4 , and^= $ i + U e 2 J
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