If the planes `vec(r).(hat(i)+2hat(j)+3hat(k))=7andvec(r).(lambdahat(i)+2hat(j)-7hat(k))=26` are perpendicular. Find the value of `lambda.`

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

If the planes vec(r)*(2hat(i)-lamdahat(j)+hat(k))=3andvec(r)(4hat(i)+hat(j)-muhat(k))=5 are parallel, then the value of lambdaandmu are

Find the parametric form of vector equation, and Cartesian equations of the plane containing the line vec(r)=(hat(i)-hat(j)+3hat(k))+t(2hat(i)-hat(j)+4hat(k))" and perpendicular to plane "vec(r)*(hat(i)+2hat(j)+hat(k))=8.

The volume of the parallelepiped whose coterminus edges are 7hat(i)+lambdahat(j)-3hat(k),hat(i)+2hat(j)-hat(k)-3hat(i)+7hat(j)+5hat(k) is 90 cubic units. Find the value of lambda.

If vec(a)=2hat(i)+3hat(j)-hat(k),vec(b)=hat(i)+2hat(j)-5hat(k),vec(c)=3hat(i)+5hat(j)-hat(k), then a vector perpendicular to vec(a) and lies in the plane containing vec(b)andvec(c) is

If vectors vec a= hat i+2 hat j- hat k , vec b=2 hat i- hat j+ hat ka n d vec c="lambda" hat"i"+ hat"j"+2 hat"k" are coplanar, then find the value of (lambda-4)dot

Thescalar product of the vector hat i + hat j + hat k with a unit vector along the sum of vectors 2 hat i + 4 hat j - 5 hat k and lambda hat i + 2 hat j + 3 hat k is equal to one. Find the value of lambda .

Show that the straight lines vec(r)=(5hat(i)+7hat(j)-3hat(k))+s(4hat(i)+4hatj-5hat(k))andvec(r)=(8hat(i)+4hat(j)+5hat(k))+t(7hat(i)+hat(j)+hat(k)) are coplanar. Find the vector equation of the plane in which they lie.