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Let the plane ax +by+cz+d=0 bisect the l...

Let the plane `ax +by+cz+d=0` bisect the line joining the points (4, -3,1) and (2, 3, -5) at the right angles। If a, b, c, d are integers, then the minimum value of `(a^2 + b^2 + c^2 + d^2)` is_______.

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The equation of the plane, which bisects the line joining the points (1, 2, 3) and (3, 4, 5) at right angles, is

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Knowledge Check

  • The equation of the plane, which bisects the line joining the points (1, 2, 3) and (3, 4, 5) at right angles, is

    A
    `x+y+z=0`
    B
    `x+y-z=0`
    C
    `x+y+z=9`
    D
    `x+y-z+9=0`

  • The intercepts made on the axes by the plane which bisects the line joining the points (1, 2, 3) and (-3,4,5) at right angle, are

    A
    `(-9/2,9,9)`
    B
    `(9/2,-9,9)`
    C
    `(19,-9/2,9)`
    D
    `(9,9/2,19)`

  • Equation of the plane which bisects the join of the points A(3,-1,4) and B(-3,5,2) at right angles is

    A
    3x-3y+z+3=0
    B
    3x-3y-z+3=0
    C
    3x+3y+z=3
    D
    3x+3y-z=3
    • JEE MAINS PREVIOUS YEAR-JEE MAIN 2021-MATHEMATICS SECTION B
    1. Let the plane ax +by+cz+d=0 bisect the line joining the points (4, -3,...

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    2. The mean age of 25 teachers in a school is 40 years। A teacher retires...

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    3. The number of times the digit 3 will be written when listing the integ...

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    4. A square ABCD has all its vertices on the curve x^2y^2=1. The midpoint...

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    5. The missing value in the following figurs is .

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    6. The equation of the planes parallel to the plane x - 2y + 2z - 3=0 whi...

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    7. The number of sotutions of the equation abs(cotx)=cotx+1/(sinx) " in t...

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    8. Let f(x) and g(x) be two functions satisfying f(x^(2))+g(4-x)=4x^(3),...

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    9. Let z1,z2 be the roots of the equation z^2+az+12=0 and z1, z2 form an ...

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    10. If f(x)=int(5x^8+7x^6)/((x^2+1+2x^7)^2)dx, (xge0), f(0)=0 and f(1)=1/K...

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    11. Let the coefficients of third, fuurth and fifth terms in the expansion...

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    12. Let vecx be a vector in the plane containing vectors veca=2hati-hatj+h...

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    13. Let I(n)= int(1)^(e ) x^(19) (log|x|)^(n)dx, where n in N. If (20)I(10...

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    14. Let tan alpha, tan beta and tan gamma, alpha, beta, gamma ne ((2n-1)pi...

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    15. Let f:[-3,1] toR be given as f(x)={("min" {(x+6)","x^(2)}",", -3 le ...

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    16. If 1, log(10)(4^(x)-2) and log(10)(4^(x)+(18)/(5)) are in arithmetic...

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    18. Consider a set of 3n numbers having variance 4. In this set, the mean ...

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    19. Let A=[(a,b),(c, d)]and B=[(alpha), (beta)] ne [(0), (0)] such that AB...

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    20. Let f:[-1, 1] to R be defined as f(x)=ax^(2)+bx+c for all x in [-1, 1]...

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