Find the position vector of a point which divides the join of points with position vectors and externally in the ratio 2 : 1.
Write the position vector of the point which divides the join of points with position vectors and in the ratio 2:1.
L and M are two points with position vectors and respectively. Write the position vectors of a point N which divides the line segment LM in the ratio 2:1 externally.
P and Q are two points with position vectors and respectively. Write the position vector of a point R which divides the line segment PQ externally in the ratio 2 : 1.
The position vectors of points A, B and C are , and respectively. If C divides the line segment joining A and B in the ratio 3 : 1, find the values of λ and μ.
Write a unit vector in the direction of vector where and are the points (1, 3, 0) and (4, 5, 6),respectively,
Show that the relation R on the set Z of all integers defined by (x, y) ∈ is divisible by 3 is an equivalence relation.
If Z is the set of all integers and R is the relation on Z defined as R = {(a, b) : a, b ∈ Z and a – b is divisible by 5}. Prove that R is an equivalence relation.
A and B throw a pair of dice alternatively, till one of them gets a total of 10 and wins the game. Find their respective probabilities of winning, if A starts first.
Two farmers X and Y cultivate only three varieties of rice namely Basmati, Permal and Naura. The sale in rupees of these varieties of rice by both the farmers in the months of September and October are given by the following matrices A and B.