Show that the points A(1,2,8) , B(5,0,2) and C(11,3,7)are collinear, and find the ratio in which B divides AC.
If in parallelogram ABCD, diagonal vectors are AC=2i^+3j^+4k^ and BD=−6i^+7j^−2k^, then find the adjacent side vectors AB and AD
Find the resultant of vectors a=i^−j^+2k^andb=i^+2j^−4k^˙ Find the unit vector in the direction of the resultant vector.
Let x2+3y2=3 be the equation of an ellipse in the x−y plane. AandB are two points whose position vectors are −3i^and−3i^+2k^˙ Then the position vector of a point P on the ellipse such that ∠APB=π/4 is a. ±j^ b. ±(i^+j^) c. ±i^ d. none of these
Let us define the length of a vector ai^+bj^+ck^as∣a∣+∣b∣+∣c∣˙ This definition coincides with the usual definition of length of a vector ai^+bj^+ck^ is and only if a. a=b=c=0 b. any two of a,b,andc are zero c. any one of a,b,andc is zero d. a+b+c=0