The position vector of a point P is `r=xhat(i)+yhat(j)+hat(k)z,` where `x, y, zinN and a=hat(i)+2hat(j)+hat(k). If r*a=20` and the number of possible of P is `9lambda`, then the value of `lambda` is

The position vector of a point P is vecr=xhat(i)+yhat(j)+zhat(k), where x, y, zinN and veca=hat(i)+2hat(j)+hat(k). If vecr*veca=20 and the number of possible of P is 9lambda , then the value of lambda is:

The position vector of a point P is vecr=xhat(i)+yhat(j)+zhat(k), where x, y, zinN and veca=hat(i)+2hat(j)+hat(k). If vecr*veca=20 and the number of possible of P is 9lambda , then the value of lambda is:

If vec(r)=xhat(i)+yhat(j)+zhat(k) , then what is vec(r).(hat(i)+hat(j)+hat(k)) equal to?

The position vector of a point is R =x hat i +y hat j + z hat k and another vector is A =3 hat i +2 hat j + 5hat k .Which of the mathematical relations is correct ?

The co-ordinate of the point P on the line r=(hat(i)+hat(j)+hat(k))+lambda(-hat(I)+hat(j)-hat(k)) which is nearest to the origin is

The co-ordinate of the point P on the line r=(hat(i)+hat(j)+hat(k))+lambda(-hat(I)+hat(j)-hat(k)) which is nearest to the origin is

If the vectors p hat(i)+hat(j)+hat(k), hat(i)+q hat(j)+hat(k) and hat(i)+hat(j)+r hat(k) (p ne q ne r ne 1) are coplanar, then the value of pqr -(p+q+r) is :

If vec(a) = xhat(i) + 2hat(j) - z hat(k) and vec(b) = 3hat(i) - y hat(j) + hat(k) are two equal vectors, then find the value of x + y +z.

If the planes overset(to)( r) (2 hat(i) - lambda (j) + 3 hat(k) ) = 0 and overset(to)( r) ( lambda (i) + 5 hat(j) - hat(k) )=5 are perpendicular to each other, then the value of lambda is