Find the vector equation of the plane `vecr = 2 hati + hatj - 3 hatk + lamda ( 2hatj +hatk) + mu(5 hati + 2 hatj + hatk)` in scalar product form.

Vector equation of the plane r = hati-hatj+ lamda(hati +hatj+hatk)+mu(hati – 2hatj+3hatk) in the scalar dot product form is

Convert the equation of the plane vecr = (hati-hatj)+lambda(-hati+hatj+2hatk)+mu(hati+2hatj+hatk) into scalar product form.

Find the vector equation of the following plane in product form vecr = ( hati-hatk)+lambda(hati+2hatj)+mu(hati+3hatj-hatk) .

The line whose vector equation are vecr =2 hati - 3 hatj + 7 hatk + lamda (2 hati + p hatj + 5 hatk) and vecr = hati - 2 hatj + 3 hatk+ mu (3 hati - p hatj + p hatk) are perpendicular for all values of gamma and mu if p equals :

If the point of intersection of the line vecr = (hati + 2 hatj + 3 hatk ) + lambda( 2 hati + hatj+ 2hatk ) and the plane vecr (2 hati - 6 hatj + 3 hatk) + 5=0 lies on the plane vec r ( hati + 75 hatj + 60 hatk) -alpha =0, then 19 alpha + 17 is equal to :

Find the vector equation of the following planes in cartesian form : " "vecr=hati-hatj+lamda(hati+hatj+hatk)+mu(hati-2hatj+3hatk) .

Find the points of intersection of the line vecr = (2hati - hatj + 2hatk) + lambda(3hati + 4hatj + 2hatk) and the plane vecr.(hati - hatj + hatk) = 5

Find the shortest distance between the lines vecr = 2hati - hatj + hatk + lambda(3hati - 2hatj + 5hatk), vecr = 3hati + 2hatj - 4hatk + mu(4hati - hatj + 3hatk)

The vector equation of the plane containing he line vecr=(-2hati-3hatj+4hatk)+lamda(3hati-2hatj-hatk) and the point hati+2hatj+3hatk is

The line vecr = 2hati - 3 hatj - hatk + lamda ( hati - hatj + 2 hatk ) lies in the plane vecr. (3 hati + hatj - hatk) + 2=0 or not