Important Questions of Three Dimensional Geometry Mathematics | Zigya
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    Mathematics : Three Dimensional Geometry

    Multiple Choice QuestionsShort Answer Type

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    251. Find the angle between the line fraction numerator straight x minus 1 over denominator 1 end fraction space equals space fraction numerator straight y minus 2 over denominator negative 1 end fraction space equals space fraction numerator straight z plus 1 over denominator 1 end fraction and the plane 2x – y + z= 1. 
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    252.

    Find the angle between the line fraction numerator straight x plus 1 over denominator 3 end fraction space equals space fraction numerator straight y minus 1 over denominator 2 end fraction space equals space fraction numerator straight z minus 2 over denominator 4 end fraction and the plane 2x + y – 3z + 4 = 0.

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    253. Find the angle between the lines fraction numerator straight x plus 1 over denominator 2 end fraction space equals space straight y over 3 space equals space fraction numerator straight z minus 3 over denominator 6 end fraction and the plane 10x + 2y – 11z = 3.
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    254. Find the angle between the line fraction numerator straight x minus 2 over denominator 3 end fraction space equals space fraction numerator straight y plus 1 over denominator negative 1 end fraction space equals space fraction numerator straight z minus 3 over denominator 2 end fraction and the plane 3x + 4y + z + 5 = 0.
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    255.

    Find the angle between the line straight r with rightwards arrow on top space equals space open parentheses straight i with hat on top space minus space straight j with hat on top space plus space straight k with hat on top close parentheses space plus space straight lambda space open parentheses 2 straight i with hat on top space minus space straight j with hat on top space plus space 3 space straight k with hat on top close parentheses and the plane straight r with rightwards arrow on top. space open parentheses 2 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 space equals space 4

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    256. Find the distance between the parallel planes:
    2x – 3y + z + 3 = 0
    and 4x – 6y + 2z + 5 = 0
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    257. Find the distance between parallel planes:
    2x  – y + 3z – 4 = 0 and 6x – 3y + 9z + 13 = 0.
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    258. Find the distance between the planes straight r with rightwards arrow on top. space open parentheses straight i with hat on top space plus space 2 space straight j with hat on top space plus space space 3 space straight k with hat on top close parentheses space plus space 7 space equals 0 and straight r with rightwards arrow on top. space open parentheses 2 straight i with hat on top space plus space 4 space straight j with hat on top space plus space 6 space straight k with hat on top close parentheses space plus space 7 space equals space 0.
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    Multiple Choice QuestionsLong Answer Type

    259. Find the length and coordinates of the foot of the perpendicular from the point (1, 1, 2) to the plane 2x – 2y + 4z + 5 = 0.
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    260. Find the distance between the point P(6, 5, 9) and the plane determined by the points A(3, –1, 2), B(5, 2, 4) and C(– 1, – 1, 6).
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