Question

The line passing through the points (5, 1, a) and (3, b, 1) crosses the yz−plane at the point $open parentheses 0 space comma 17 over 2 comma space fraction numerator negative 13 over denominator 2 end fraction close parentheses$ . Then

a = 2, b = 8

a = 4, b = 6

a = 6, b = 4

a = 8, b = 2

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Solution

a = 6, b = 4

fraction numerator straight x minus 5 over denominator 2 end fraction space equals space fraction numerator straight y minus 1 over denominator 1 minus straight b end fraction space equals space fraction numerator straight z minus straight a over denominator straight a minus 1 end fraction space equals space straight lambda if space line space crosses space yz minus plane space straight i. straight e. comma space straight x space equals 0 straight x space equals space 2 straight lambda space plus 5 space equals space 0 rightwards double arrow space 2 straight lambda space plus space 5 space equals space 0 rightwards double arrow space straight lambda space equals space minus space 5 divided by 2 since comma space straight y space equals space straight lambda left parenthesis 1 minus straight b right parenthesis space plus space 1 space equals space 17 over 2 minus 5 over 2 space left parenthesis 1 minus straight b right parenthesis space plus space 1 space equals space minus 17 over 2 straight b space equals space 4 also comma space straight z space equals space straight lambda space left parenthesis straight a minus 1 right parenthesis space plus straight a space equals space minus space 13 over 2 fraction numerator negative 5 over denominator 2 end fraction space left parenthesis straight a minus 1 right parenthesis space plus straight a space equals space minus space 13 over 2 rightwards double arrow straight a space equals space 6

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