The Cartesian equation of the plane ` vec r=(1+lambda-mu) hat i+(2-lambda) hat j+(3-2lambda+2mu) hat k` is a. `2x+y=5` b. `2x-y=5` c. `2x+z=5` d. `2x-z=5`

The cartesian eqaution of the plane r=(1+lambda-mu)hat(i)+(2-lambda)hat(j)+(3-2lambda+2mu)hat(k) , is

Find the vector equation of the following planes in non parametric form: -> r=(lambda-2mu) hat i+(3-mu) hat j+(2lambda+mu) hat k

Find the shortest distance between the lines vec r=(1-lambda)hat i+(lambda-2)hat j+(3-2 lambda)hat k and vec r=(mu+1)hat i+(2 mu+1)hat k

Find the vector equation of the following planes in non- parametric form: (i) vec r=(lambda-2 mu)hat i+(3-mu)hat j+(2 lambda=mu)hat k.(ii)vec r=(2hat i+2hat j-hat k)+lambda(hat i+2hat j+3hat k)+mu(5hat i-2hat j+7hat k)

Find the vector equation of the plane vec r=2hat i+hat j-3hat k+lambda(2hat j+hat k)+mu(5hat i+2hat j+hat k) in scalar product form.

Find the shortest distance between the following two lines: vec r=(1+lambda)hat i+(2-lambda)hat j+(lambda+1)hat kvec r=(2hat i-hat j-hat k)+mu(2hat i+hat j+2hat k)

Vector equation of the plane r=hat i-hat j+lambda(hat i+hat j+hat k)+mu(hat i2hat j+3hat k) in the scalar dot product form is

Find the vector and Cartesian equations of the plane containing the two lines vec r=2hat i+hat j-3hat k+lambda(hat i+2hat j+5hat k) and vec r=3hat i+3hat j+2hat k+mu(3hat i-2hat j+5hat k)

ABCD is a rhombus.If vec AC=hat i+(1+lambda)hat j+(lambda-2)hat k and vec BD=(2 lambda-1)hat i+hat j-hat k then lambda=