If `vecr = hati + hatj + lamda( 2 hati + hatj + 4 hatk ) and vecr (hati + 2 hatj - hatk)=3` are the equations of a line and a plane respectively then which of the following is true ?

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

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 vecr=(hati+2hatj+3hatk)+lambda(hati-hatj+hatk) and vecr=(hati+2hatj+3hatk)+mu(hati+hatj-hatk) are two lines, then the equation of acute angle bisector of two lines is

The angle between the planes vecr. (2 hati - 3 hatj + hatk) =1 and vecr. (hati - hatj) =4 is

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 :

If the planes vecr.(2hati-hatj+2hatk)=4 and vecr.(3hati+2hatj+lamda hatk)=3 are perpendicular then lamda=

If vecr=(hati+2hatj+3hatk)+lamda(hati-hatj+hatk) and vecr=(hati+2hatj+3hatk)+mu(hati+hatj-hatk) are two lines, then find the equation of acute angle bisector of two lines.

If vecomega=2hati-3hatj+4hatk and vecr=2hati-3hatj+2hatk then the linear velocity is

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

The angle between the planes vecr.(2hati-hatj+hatk)=6 and vecr.(hati+hatj+2hatk)=5 is