If the line `vec r-2hati-hatj+3hatk+lambda(hati+hatj+sqrt2hatk)` makes angles `alpha,beta,gamma` with `xy,yz and zx` planes respectively then which of the following are not possible?

If barr=hati+hatj+lambda(2hati+hatj+4hatk)" and "barr*(hati+2hatj-hatk)=3 are the equations of a line and plane respectively, then which of the following is truwe?

Angle between the line vecr=(2hati-hatj+hatk)+lamda(-hati+hatj+hatk) and the plane vecr.(3hati+2hatj-hatk)=4 is

Angle between the line vecr=(2hati-hatj+hatk)+lamda(-hati+hatj+hatk) and the plane vecr.(3hati+2hatj-hatk)=4 is

Angle between the line vecr=(2hati-hatj+hatk)+lamda(-hati+hatj+hatk) and the plane vecr.(3hati+2hatj-hatk)=4 is

(i) Find the distance of the point (-1,-5,-10) from the point of intersection of the line vec(r) = (2 hati - hatj + 2 hatk ) + lambda (3 hati + 4 hatj + 12 hatk) and the plane vec(r).(hati - hatj + hatk) = 5. (ii) Find the distance of the point with position vector - hati - 5 hatj - 10 hatk from the point of intersection of the line vec(r) = (2 hati - hatj + 2 hatk ) + lambda (3 hati + 4 hatj + 12 hatk ) and the plane vec(r). (hati - hatj + hatk)= 5. (iii) Find the distance of the point (2,12, 5) from the point of intersection of the line . vec(r) = 2 hati - 4 hatj + 2 hatk + lambda (3 hati + 4 hatj + 12 hatk ) and the plane vec(r). (hati - 2 hatj + hatk ) = 0.

Find the angle between the line vecr=(2hati-hatj+3hatk)+lambda(3hati-hatj+2hatk) and the plane vecr.(hati+hatj+hatk)=3 .

The lines barr=hati+2hatj+3hatk+lambda(hati+2hatj+3hatk) and barr=-2hatj+hatk+lambda(2hati+2hatj-2hatk) are

Show that the line vecr=hati+hatj+lambda(2hati+hatj+4hatk) lies in the plane vecr.(hati+2hatj-hatk)=3