समतल का कार्तीय समीकरण गया कीजिए|
` vecr . ( 2hati + 3hatj -4hatk ) =1`

The line of intersection of the planes vecr . (3 hati - hatj + hatk) =1 and vecr. (hati+ 4 hatj -2 hatk)=2 is:

Find the angle between the line vecr = (hati +2hatj -hatk ) +lambda (hati - hatj +hatk) and vecr cdot (2hati - hatj +hatk) = 4.

Prove that the equaton of a plane through point (2,-4,5) and the line o lintersection of the planes vecr.(2hati+3hatj-4hatk) = 1 and vecr.(3hati+hatj-2hatk) = 2 is vecr.(2hati+8hatj+7hatk) = 7 .

Find the vector equation of the plane passing through the intersection of the planes vecr cdot (hati+hatj+hatk) = 6 and vecr cdot(2hati + 3hatj+4hatk) = -5 , and the point (1, 1, 1).

Given that vecu = hati - 2hatj + 3hatk , vecv = 2hati + hatj + 4hatk , vecw = hati + 3hatj + 3hatk and (vecu.vecR - 15) hati + (vecv. vecR - 30) hatj + (vecw . vecR - 20) veck = 0 . Then find the greatest integer less than or equal to |vecR| .

Find the equation of the plane through the line of intersection of vecr.(2hati-3hatj+4hatk)=1 and vecr.(hati-hatj)+4=0 and perpendicular to vecr.(2hati-hatj+hatk)+8=0

Given that vecu = hati + 2hatj + 3hatk , vecv = 2hati + hatk + 4hatk , vecw = hati + 3hatj + 3hatk and (vecu.vecR - 15) hati + (vecc. vecR - 30) hatj + (vecw . vec- 20) veck = vec0 . Then find the greatest integer less than or equal to |vecR| .

Given that vecu = hati + 2hatj + 3hatk , vecv = 2hati + hatk + 4hatk , vecw = hati + 3hatj + 3hatk and (vecu.vecR - 15) hati + (vecc. vecR - 30) hatj + (vecw . vec- 20) veck = vec0 . Then find the greatest integer less than or equal to |vecR| .

Find the shortest distance between the lines vecr =lambda (2hati+ 3hatj+4hatk) and vecr=(hati-hatj)+t(2hati-3hatj+4hatk)