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Find the equation of the plane passing t...

Find the equation of the plane passing through the line of intersection of the planes `vec(r)*(2hat(i)-7hat(j)+4hat(k))=3and3x-5y+4z+11=0," and the point "(-2,1,3).`

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Find the angle between the planes vec(r)*(hat(i)+hat(j)-2hat(k))=3and2x-2y+z=2

Find the equation of the plane passing through (3,4,-1), which is parallel to the plane vec rdot(2 hat i-3 hat j+5 hat k)+7=0.

Knowledge Check

  • For the plane vec(r).(2hat(i)+3hat(j)+5hat(k))=3

    A
    the normal vector is `2hat(i)+3hat(j)+5hat(k)`
    B
    the plane is `bot` to the vector `2hat(i)+3hat(j)+5hat(k)`
    C
    cartesain equation is 2x + 3y +5z = 3
    D
    the plane is parallel to the vector `2hat(i)+3hat(j)+5hat(k)`

  • The distance from the origin to he plane vec(r)(2hat(i)-hat(j)+5hat(k))=7 is ……………

    A
    `(7)/(sqrt(30))`
    B
    `(sqrt(30))/(7)`
    C
    `(30)/(7)`
    D
    `(7)/(30)`

  • The coordinates of the point where the line vec(r)=(6i-j-3k)+t(-i+4k)" meets the plane "vec(r)*(hat(i)+hat(j)-hat(k))=3 are

    A
    `(1,2,-6)`
    B
    `(7,-1,-7)`
    C
    `(1,2,-6)`
    D
    `(5,-1,1)`

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    Explore conceptually related problems

    Find the equation the plane which contain the line of intersection of the planes vec rdot( hat i+2 hat j+3 hat k)-4=0a n d vec rdot(2 hat i+ hat j- hat k)+5=0 and which is perpendicular to the plane vec r(5 hat i+3 hat j-6 hat k)+8=0 .

    Find the intercept cut off by the plane vec(r)=(6hat(i)+4hat(j)-3hat(k))=12 on the coordinate axes.

    Find the vector and Cartesian equations of the plane passing through the point with position vector 2hat(i)+6hat(j)+3hat(k)" and normal to the vector "hat(i)+3hat(j)+5hat(k).

    Find the vector equation of the line passing through (1,2,3) and parallel to the planes vec rdot( hat i- hat j+2 hat k)a n d vec rdot(3 hat i+ hat j+ hat k)=6.

    Find the vector equation of the line passing through (1, 2, 3 ) and parallel to the planes -> rdot( hat i- hat j+2 hat k)=5\ a n d\ -> rdot(3 hat i+ hat j+ hat k)=6.

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