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Find the equation of the plane which co...

Find the equation of the plane which contains the line of intersection of the planes ` vecr cdot( hat i+2 hat j+3 hat k)-4=0, vecr cdot(2 hat i+ hat j- hat k)+5=0`and which is perpendicular to the plane `vecr.(5hati+3hatj-6hatk)+8=0`

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To find the equation of the plane that contains the line of intersection of the given planes and is perpendicular to another plane, we will follow these steps: ### Step 1: Identify the equations of the given planes The equations of the two planes are: 1. \( P_1: \vec{r} \cdot (\hat{i} + 2\hat{j} + 3\hat{k}) - 4 = 0 \) 2. \( P_2: \vec{r} \cdot (2\hat{i} + \hat{j} - \hat{k}) + 5 = 0 \) ### Step 2: Find the normal vectors of the planes ...
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Find the equation of the plane which contains the line of intersection of the planes vec r .(hat i+2hat j+3hat k)-4=0,vec r*(2hat i+hat j-hat k)+5=0 and which is perpendicular to the plane vec r*(5hat i+3hat j-6hat k)+8=0

Find the vector equation of the plane which contains the line of intersection of the plane vec r*(hat i+2hat j+3hat k)-4=0 and vec r*(2hat i+hat j-hat k)+5=0 and which is perpendicular to the plane vec r*(5hat i+3hat j-6hat k)+8=0

Find the equation of the plane which contains the line of intersection of the planes vec r*(hat i+2hat j+3hat k)-1=0,vec r*(2hat i+hat k-hat k)+5=0 and which is perpendicular to the plane vec r.(5hat i+3hat j-6hat k)+8=0

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

17.Find the the equation of the plane which contains the line of intersection of the planes vec r*(hat i+2hat j+3hat k)-4=0,vec r*(2hat i+hat j-hat k)+5=0* and which is perpendicular to the vec r.(5hat i+3hat j-6hat k)+8=0

(i) Find the vector equation of the plane through the intersection of the planes : vec(r) . (hati + hatj + hatk) = 6, vec(r) . (2 hati + 3 hatj + 4 hatk) = -5 and the point (1,1,1). (ii) Find the equation of the plane which contains the line of intersection of the planes : vec(r) . (hat(i) + 2 hat(j) + 3 hat(k) ) - 4 = 0. vec(r). (2 hat(i) + hatj - hat(k) ) + 5 = 0 and which is perpendicular to the plane : vec(r) . (5 hati + 3 hatj - 6 hatk ) + 8 = 0 . (iii) Find the equation the plane passing through the intersection of the planes x + y + z = 6 and 2x + 3y + 4z + 5 = 0 and the point (1,1,1) .

Find the equation of the plane through the line of intersection of the planes vec rdot(( hat i+3 hat j)+6=0\ a n d\ vec rdot((3 hat i- hat j-4 hat k)=0, which is at a unit distance from the origin.

Find the equation of the plane passing through the intersection of the planes vec rdot( (hat i+ hat j+ hat k)=1\ a n d\ vec rdot((2 hat i+3 hat j- hat k)+4=0 and parallel to x-axis.

Find the equation of the plane passing through the line of intersection of the planes vec r*(hat i+hat j+hat k)=1 and vec r*(2hat i+3hat j-hat k)+4=0 and parallel to x-axis.

Find the equation of the plane which contains the line of intersection of the planes: vec(r). (hat(i) - 2 hat(j) + 3 hat(k) ) - 4 = 0 and vec(r). ( - 2 hat(i) + hat(j) + hat(k)) + 5 = 0 and whose intercept on x-axis is equal to that of y-axis.

NCERT-THREE DIMENSIONAL GEOMETRY-MISCELLANEOUS EXERCISE
  1. Find the equation of the plane passing through the line of intersecti...

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  2. If the points (1,1,p) a n d (3, 0, 1)be equidistant from the plane v...

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  3. Find the equation of the plane which contains the line of intersectio...

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  4. If O be the origin and the coordinates of P be(1, 2, -3), then find ...

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  5. Find the coordinates of the point where the line through (5, 1, 6) an...

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  6. Find the coordinates of the point where the line through (5, 1, 6) an...

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  7. Find the equation of the plane passing through the point ( 1, 3, 2)an...

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  8. Find the coordinates of the point where the line through (3, 4, 5)a...

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  9. The planes: 2x y + 4z = 5 a n d 5x 2. 5 y + 10 z = 6are(A) Perpendic...

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  10. Find the equation of the plane passing through (a, b, c) and parallel...

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  11. Find the shortest distance between lines vecr=6 hat i+2 hat j+ hat k...

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  12. If the lines (x-1)/(-3)=(y-2)/(2k)=(z-3)/2and (x-1)/(3k)=(y-1)/1=(z-6...

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  13. Find the vector equation of the line passing through (1, 2, 3) and pe...

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  14. Find the equation of a line parallel to x-axis and passing through th...

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  15. If the coordinates of the points A, B, C, D be (1, 2, 3), (4, 5, 7),...

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  16. If l1,m1,n1and l2,m2,n2are the direction cosines of two mutually per...

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  17. Find the angle between the lines whose direction ratios are a, b, c a...

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  18. Show that the line joining the origin to the point (2, 1, 1)is perpen...

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  19. Find the vector equation of the line passing through the point (1,2,-...

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  20. Prove that if a plane has the intercepts a, b, c and is at a distance...

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