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

Long Answer Type

281. Find the vector and cartesian equation of the plane containing the two lines

straight r with rightwards arrow on top space equals space 2 space straight i with hat on top space plus space straight j with hat on top space minus space 3 space straight k with hat on top space plus space straight lambda space left parenthesis straight i with hat on top space plus space 2 space straight j with hat on top space plus space 5 space straight k with hat on top right parenthesis

and

straight r with rightwards arrow on top space equals space 3 space straight i with hat on top space plus space space 3 space straight j with hat on top space minus space 7 space straight k with hat on top space plus space straight mu space left parenthesis 3 straight i with hat on top space minus space 2 space straight j with hat on top space plus space space 5 space straight k with hat on top right parenthesis

72 Views

Short Answer Type

282. Find the equation of the plane containing the lines:

fraction numerator straight x minus 4 over denominator 1 end fraction space equals space fraction numerator straight y minus 3 over denominator 4 end fraction space equals space fraction numerator straight z minus 2 over denominator 5 end fraction

and

fraction numerator straight x minus 3 over denominator 1 end fraction space equals space fraction numerator straight y minus 2 over denominator negative 4 end fraction space equals space straight z over 5

82 Views

Long Answer Type

283. Find the equation of the plane passing through the points (3, 2, 1) and (0, 1, 7) and parallel to the line

straight r with rightwards arrow on top space equals space 2 space straight i with hat on top space minus space straight j with hat on top space plus space straight k with hat on top space plus space straight lambda left parenthesis straight i with hat on top space minus space straight j with hat on top space minus space straight k with hat on top right parenthesis.

74 Views

284. Find the equation of the plane passing through the points (1, 2, 3) and (0. –1, 0) and parallel to the line

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

87 Views

285. Find the equation of the plane passing through the points (3, 2, 2) and (1, 0, –1) parallel to the line

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

108 Views

286. Find the equation of the plane passing through the origin and parallel to the vectors

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

97 Views

Short Answer Type

287. Find the vector and Cartesian form of the equation of the plane passing through the point (1, 2, –4) and parallel to the lines
$straight r with rightwards arrow on top space equals straight i with hat on top space plus space 2 space straight j with hat on top space minus space 4 space straight k with hat on top space plus space straight lambda open parentheses 2 straight i with hat on top space plus space 3 space straight j with hat on top space plus space 6 space straight k with hat on top close parentheses$
and $straight r with rightwards arrow on top space equals space straight i with hat on top space minus space 3 space straight j with hat on top space plus space space 5 space straight k with hat on top space plus space straight mu space open parentheses straight i with hat on top space plus space straight j with hat on top space minus space straight k with hat on top close parentheses$

Here, $straight a with rightwards arrow on top space equals space straight i with hat on top space plus space 2 space straight j with hat on top space minus space 4 straight k with hat on top comma space space space straight b with rightwards arrow on top space equals space 2 straight i with hat on top space plus space 3 space straight j with hat on top space plus space 6 space straight k with hat on top comma space space straight c with rightwards arrow on top space equals space straight i with hat on top space plus space straight j with hat on top space minus space straight k with hat on top$
The vector equation of plane is
$open parentheses straight r with rightwards arrow on top minus straight a with rightwards arrow on top close parentheses. space open parentheses straight b with rightwards arrow on top space cross times space straight c with rightwards arrow on top close parentheses space equals 0$
$or space space space space open square brackets straight r with rightwards arrow on top space minus space left parenthesis straight i with hat on top space plus space 2 space straight j with hat on top space minus space 4 space straight k with hat on top right parenthesis close square brackets space. space open square brackets left parenthesis 2 space straight i with hat on top space plus space 3 space straight j with hat on top space plus space 6 space straight k with hat on top right parenthesis space cross times space left parenthesis straight i with hat on top space plus space straight j with hat on top space minus space straight k with hat on top right parenthesis close square brackets space equals space 0$
Cartesian equation of plane is
$open vertical bar table row cell straight x minus 1 end cell cell straight y minus 2 end cell cell straight z plus 4 end cell row 2 3 6 row 1 1 cell negative 1 end cell end table close vertical bar space equals space 0$
or $left parenthesis straight x minus 1 right parenthesis space open vertical bar table row 3 6 row 1 cell negative 1 end cell end table close vertical bar space minus space left parenthesis straight y minus 2 right parenthesis space open vertical bar table row 2 6 row 1 cell negative 1 end cell end table close vertical bar space plus space left parenthesis straight z plus 4 right parenthesis space open vertical bar table row 2 3 row 1 1 end table close vertical bar space equals space 0$

or    (–3 – 6) (x – 1) – (–2 – 6) (y – 2) + (2 – 3) (z + 4) = 0
or    –9 (x– 1) + 8 (y – 2) – (z + 4) = 0
or    –9x + 9 + 8y –16-z – 4 = 0
or    –9 x + 8 y – z – 11 = 0 or 9 x – 8 y + z + 11 = 0.

87 Views