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Determine or find out if the sets of vectors are parallel or not.
(a) a→ = (2,-4,1), b = (-6, 12 , -3)
(b) a→ = (4,10), b = (2,9)
Solution
(a) These two vectors are parallel as b→ = -3a→
(b) These two vectors are not parallel. This can be observed by noticing that 4 (1/2) = 2 and yet 10(1/2) = 5≠ - 9. Alternatively we can't make a? be a scalar multiple of b→.
Formulas of Surface Area - Applications of integrals S = ∫ 2Πyds rotation about x-axis S = ∫ 2Πxds rotation about y-axis Where, ds = √ 1 + (1+ (dy /
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a part of a line with two end points.
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