Let the position vectors of the points `Pa n dQ` be `4 hat i+ hat j+lambda hat ka n d2 hat i- hat j+lambda hat k ,` respectively. Vector ` hat i- hat j+6 hat k` is perpendicular to the plane containing the origin and the points `Pa n dQ` . Then `lambda` equals `1//2` b. `1//2` c. `1` d. none of these

If the position vectors of the point A and B are 3hat(i)+hat(j)+2hat(k) and hat(i)-2hat(j)-4hat(k) respectively. Then the eqaution of the plane through B and perpendicular to AB is

The position vectors of the point A,B,C and D are 3hat i-2hat j-hat k,2hat i+3hat j-4hat k,-hat i+hat j+2hat k and 4hat i+5hat j+lambdahat j, respectively.If the points A,B,C and D lie on a plane,find the value of lambda.

The position vector of the points Pa n dQ are 5 hat i+7 hat j-2 hat k and -3 hat i+3 hat j+6 hat k , respectively. Vector vec A=3 hat i- hat j+ hat k passes through point P and vector vec B=-3 hat i+2 hat j+4 hat k passes through point Q . A third vector 2 hat i+7 hat j-5 hat k intersects vectors Aa n dBdot Find the position vectors of points of intersection.

If -> a=2 hat i+2 hat j+3 hat k , -> b=- hat i+2 hat j+ hat k and -> c=3 hat i+ hat j are such that -> a+lambda -> b is perpendicular to -> c , then find the value of lambda .

Let A,B,C be points with position vectors 2hat i-hat j+hat k,hat hat i+2hat j+hat k and 2hat i+hat j+2hat k respectively.Find the shortest distance between point B and plane OAC.

A vector equally inclined to the vectors hat(i)-hat(j)+hat(k) and hat(i)+hat(j)-hat(k) then the plane containing them is

Vector equation of the plane r=hat i-hat j+lambda(hat i+hat j+hat k)+mu(hat i2hat j+3hat k) in the scalar dot product form is

If the vectors 4 hat i+11 hat j+m hat k ,\ 7 hat i+2 hat j+6 hat k\ a n d\ hat i+5 hat j+4 hat k are coplanar then m= 38 b. "\ "10"\ " c. -1 d. -10

The value of lambda for which the two vectors vec(a) = 5hat(i) + lambda hat(j) + hat(k) and vec(b) = hat(i) - 2hat(j) + hat(k) are perpendicular to each other is :

Find the vector equation of a plane passing through a point having position vector 2 hat i- hat j+ hat k and perpendicular to the vector 4 hat i+2 hat j-3 hat kdot