Previous Year Papers

Download Solved Question Papers Free for Offline Practice and view Solutions Online.

Test Series

Take Zigya Full and Sectional Test Series. Time it out for real assessment and get your results instantly.

Test Yourself

Practice and master your preparation for a specific topic or chapter. Check you scores at the end of the test.

Three Dimensional Geometry

Short Answer Type

91. Find the length of perpendicular from (2, 1, 3) on the line
$fraction numerator straight x minus 4 over denominator 5 end fraction space equals fraction numerator straight y minus 2 over denominator 4 end fraction space equals space fraction numerator straight z minus 3 over denominator 3 end fraction.$

Let the given line AB be

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

Any point M on this line is
(5 r + 4, 4 r + 2, 3 r + 3)
Let this point M be the foot of perpendicular from P(2, 1, 3) on AB.
Direction-ratios of PM are
5 r + 4 – 2, 4 r + 2 – 1, 3 r + 3 – 3 i.e. 5 r + 2, 4 r + 1, 3 r
Direction-ratios of AB are 5, 4, 3.
Since PM ⊥ AB
∴ (5 r – 2) (5) + (4 r + 1) (4) + (3 r) (3) = 0
∴ 25 r – 10 + 16 r + 4 + 9 r = 0

rightwards double arrow space space space 50 straight r space equals space 6 space space space space space space space space space space space space space space space space space space space space space space space rightwards double arrow space space straight r space equals space 3 over 25

therefore

M is

open parentheses 115 over 25 comma space 62 over 25 comma space 84 over 25 close parentheses

∴ required length of perpendicular = PM

equals space square root of open parentheses 115 over 25 minus 2 close parentheses squared plus open parentheses 62 over 25 minus 1 close parentheses squared plus open parentheses 84 over 25 minus 3 close parentheses squared end root equals space square root of open parentheses 65 over 25 close parentheses squared plus open parentheses 37 over 25 close parentheses squared plus open parentheses 9 over 25 close parentheses squared end root space equals space square root of 4245 over 625 plus 1369 over 625 plus 81 over 625 end root equals space square root of 5675 over 625 end root space equals space square root of 227 over 25 end root space equals space fraction numerator square root of 227 over denominator 5 end fraction

95 Views

92.

Find the length and foot of the perpendicular drawn from the point (3, 4, 5) on the line
$fraction numerator straight x minus 2 over denominator 2 end fraction space equals space fraction numerator straight y minus 3 over denominator 5 end fraction space equals space fraction numerator straight z minus 1 over denominator 3 end fraction$

96 Views

93.

Find the perpendicular distance of the point (1, 0, 0) form the line $fraction numerator straight x minus 1 over denominator 2 end fraction space equals space fraction numerator straight y plus 1 over denominator negative 3 end fraction space equals space fraction numerator straight z plus 10 over denominator 8 end fraction$

95 Views

94.

Find the length of the perpendicular drawn from the point (1, ,2 3) on the line
$fraction numerator straight x minus 6 over denominator 3 end fraction space equals space fraction numerator straight y minus 7 over denominator 2 end fraction space equals space fraction numerator straight z minus 7 over denominator negative 2 end fraction$