Find the value of `'lambda'` if the following planes are perpendicular.
(i) `2x-4y+3z+1 = 0` and `x +2y+lambdaz = 3`
(ii) `vecr.(3hati-6hatj-2hatk) = 1` and
`vecr.(2hati+hatj-lambdahati) = 2`

The angles between the planes vecr.(3hati-6hatj+2hatk)=4 and vecr.(2hati-hatj+2hatk)=3 , is

Find the value of lambda for which the given planes are perpendicular to the each other: i) vecr.(2hati-hatj-lambdak)=7 and vecr.(3hati+2hatj+2hatk)=9 ii) vecr.(lambdahati+2hatj+3hatk)=5 and vecr.(hati+2hatj-7hatk)+11=0

Find the angle between the planes vecr.(3hati-4hatj+5hatk)=0 and vecr.(2hati-hatj-2hatk)=7 .

Find the angles between the planes vecr(hati-2hatj-2hatk)=1 and vecr(3hati-6hatj+2hatk)=0

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

Find the angle between the folowing planes :- (i) vecr.(2hati-3hatj+4hatk) = 5 and vecr.(-hati+hatj) = 1 (ii) vecr.(2hati+3hatj-6hatk) = 1 and vecr.(hati-2hatj+2hatk) + 3 = 0 (iii) x+y-2z=3 and 2x-2y+z+1 = 0 (iv) x+y-z=8 and -x+2y+z-1 = 0

Find the angle between the folowing planes :- (i) vecr.(2hati-3hatj+4hatk) = 5 and vecr.(-hati+hatj) = 1 (ii) vecr.(2hati+3hatj-6hatk) = 1 and vecr.(hati-2hatj+2hatk) + 3 = 0 (iii) x+y-2z=3 and 2x-2y+z+1 = 0

In the following cases, determine whether the given planes are parallel or perpendicular and in case they are neither, find the angle between them. (i) 2x – y + z = 6 and x + y + 2z = 7 (ii) vecr.(hati-hatj+hatk) and vecr.(3hati+2hatj-hatk)-11=0 (iii) x + y – 2z = 3 and 2x – 2y + z = 5 (iv) 2x – 3y + 4z = 1 and -x + y = 4 (v) vecr.(2hati+3hatj-6hatk)=5 and vecr.(hat i - 2 hatj+2hatk)=9

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

Find the value of 'lambda' if the planes vecr. (hati +2hatj+3hatk)+3=0 and vecr. (lambdahati+2hatj+7hatk) = 10 are perpendicular.