Find the all the values of lamda such that `(x,y,z)!=(0,0,0)`and `x(hati+hatj+3hatk)+y(3hati-3hatj+hatk)+z(-4hati+5hatj)=lamda(xhati+yhatj+zhatk)`

The value of lambda in R such that (x, y, z) ne (0, 0, ) and (2hati+3hatj-4hatk)x+(3hati-hatj+2hatk)y+(i-2hatj)z = lambda(xhati+yhatj+zhatk) lies in

If (x,y,z) ne (0,0,0) and (hati + hatj +3hatk )x + (3 hati - 3 hatj + hatk )y +(-4 hati + 5 hatj ) z = a (x hati + y hatj + z hatk ), then the values of a are

Find the value of lamda so that the two vectors 2hati+3hatj-hatk and -4hati-6hatj+lamda hatk are parallel

Find the value of lamda such that the vectors veca=2hati+lamdahatj+hatkandvecb=hati+2hatj+3hatk are orthogonal.

Find the values of x,y and z so that vectors veca=xhati+4hatj+zhatk and vecb=3hati+yhatj+hatk are equal.

Find the value of lamda so that the two vectors 2hati+3hatj-hatk and -4hati-6hatj+lamda hatk are Perpendicular to each other

Find the shortest distance vecr=hati+2hatj+3hatk+lambda(hati-3hatj+2hatk)and vecr= 4hati+5hatj+6hatk+mu(2hati+3hatj+hatk) .

The number of distinct values of lamda , for which the vectors -lamda^(2)hati+hatj+hatk, hati-lamda^(2)hatj+hatk and hati+hatj-lamda^(2)hatk are coplanar, is

The number of distinct real values of lamda , for which the vectors -lamda^(2)hati+hatj+hatk, hati-lamda^(2)hatj+hatk and hati+hatj-lamda^(2)hatk are coplanar, is

The value of lamda for which the four points 2hati+3hatj-hatk,hati+2hatj+3hatk,3hati+4hatj-2hatk and hati-lamdahatj+6hatk are coplanar.