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Three Dimensional Geometry

Long Answer Type

131. Determine whether the following pair of lines intersect:

fraction numerator straight x minus 1 over denominator 2 end fraction space equals fraction numerator straight y plus 1 over denominator 3 end fraction space equals straight z

fraction numerator straight x plus 5 over denominator 5 end fraction space equals space fraction numerator straight y minus 2 over denominator 1 end fraction comma space space straight z space equals space 2

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Short Answer Type

132. Find the intercepts cut off by the plane x + 2y – 2z = 9 with the axes.

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133. Find the equation of the plane with intercepts 2, 3 and 4 on the x, y and z-axis respectively.

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134. Find the intercepts cut off by the plane 2x + y – z = 5.

The equation of plane is 2x + y – z = 5
or $fraction numerator 2 straight x over denominator 5 end fraction plus straight y over 5 minus straight z over 5 space equals space 1 space space space space space space space space space or space space space space space fraction numerator straight x over denominator begin display style 5 over 2 end style end fraction plus straight y over 5 plus fraction numerator straight z over denominator negative 5 end fraction space equals space 1$
which is of intercept form $straight x over straight a plus straight y over straight b plus straight z over straight c space equals space 1$ where $straight a equals 5 over 2 comma space space straight b space equals space 5 comma space space straight c space equals space minus 5.$