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Mathematics : Three Dimensional Geometry

Short Answer Type

41. The equation of a line is

fraction numerator 2 straight x minus 5 over denominator 4 end fraction space equals space fraction numerator straight y plus 4 over denominator 3 end fraction space equals fraction numerator 6 minus straight z over denominator 6 end fraction

. Find the direction cosines of a line parallel to this line.

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Long Answer Type

42. The cartesian equations of a line are 3 x + 1 = 6 y – 2 = 1 – z. Find the fixed point through which it passes, its direction ratios and also its vector equation.

92 Views

Short Answer Type

43. Find the equation of the line which passes through the point (3, 4, 5) and is parallel to the vector

2 straight i with hat on top plus 2 straight j with hat on top minus 3 straight k with hat on top.

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44. Find the vector and Cartesian equations of the line through the point (5, 2, – 4) and which is parallel to the vector

3 straight i with overparenthesis on top space plus space 2 straight j with overparenthesis on top space minus space 8 space straight k with overparenthesis on top.

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45.

Find the equation of the line which passes through the point (1, 2, 3) and is parallel to the vector $3 straight i with overparenthesis on top space plus space 2 straight j with overparenthesis on top space minus space 2 straight k with overparenthesis on top.$