The points with position vectors `60 i+3j ,40 i-8j ,a i-52 j` are collinear if a. `a=-40` b. `a=40` c. `a=20` d. none of these

The points with position vectors 60hati+3hatj, 40hati-8hatj and a hati-52 hatj are collinear if -

Prove that the points with position vectors 60hat(i)+3hat(j), 40hat(i)-8hat(j) " and " ahat(i)-52hat(j) are collinear, if a=-40.

Let P ,Q ,R and S be the points on the plane with position vectors -2i-j , 4i , 3i+3j a n d -3i+2j , respectively. The quadrilateral P Q R S must be (a) Parallelogram, which is neither a rhombus nor a rectangle (b) Square (c) Rectangle but not a square (d) Rhombus, but not a square

Given that the points with position vectors 12hat(i)-5hat(j), 10hat(i)+3hat(j) " and " xhat(i)+11hat(j) are collinear, find x.

If points hat i+ hat j , hat i- hat j and p hat i+q hat j+r hat k are collinear, then

Let x^2+3y^2=3 be the equation of an ellipse in the x-y plane. Aa n dB are two points whose position vectors are -sqrt(3) hat ia n d-sqrt(3) hat i+2 hat kdot Then the position vector of a point P on the ellipse such that /_A P B=pi//4 is a. +- hat j b. +-( hat i+ hat j) c. +- hat i d. none of these

Find the value of lambda for which the three points with position vector 3 hat i-2 hat j- hat k ,2 hat i+3 hat j-4 hat k , and4 hat i+5 hat j+lambda hat k are coplanar.

The ratio in which the line segment joining the points whose position vectors are 2 hat i-4 hat j-7 hat ka n d-3 hat i+5 hat j-8 hat k is divided by the plane whose equation is hat r.( hat i-2 hat j+3 hat k)=13 is a. 13 : 12 internally b. 12 : 25 externally c. 13 : 25 internally d. 37 : 25 internally

Let vecalpha=a hat i+b hat j+c hat k , vecbeta=b hat i+c hat j+a hat ka n d vecgamma=c hat i+a hat j+b hat k are three coplanar vectors with a!=b ,a n d vec v= hat i+ hat j+ hat kdot Then v is perpendicular to vecalpha b. vecbeta c. vecgamma d. none of these

Find the projection of vector hat i+3 hat j+7 hat k on the vector 7 hat i- hat j+8 hat kdot