Rajasthan Board RBSE Class 12 Maths Chapter 13 Vector Ex 13.1
Compute the magnitude of the following vectors :
Write two different vectors having same magnitude.
Write two different vectors having same direction.
Find the values of x and y so that the vectors 2 + 3 and x + y are equal.
Two vectors are equal if their corresponding coefficients are equal
⇒ 2 = x and 3 = y
x = 2 and y = 3.
Find the scalar and vector components of the vector with initial point (2,1) and terminal point (- 5,7).
Coordinates of initial point A are (2, 1).
and coordinates of terminal point B are (- 5, 7)
Now from formula
Find the unit vector in the direction of the vector = + + 2
Find the unit vector in the direction of vector where P and Q are the points (1,2,3) and (4,5,6).
For the given vectors,
Find the unit vector in the direction of the vector
Find a vector in the direction of vector
which has magnitude 8 units.
Show that the vectors
and are collinear.
Find the position vector of a point R which divides the line joining two points P and Q whose position vectors are
respectively in the ratio 2:1.
(i) internally (ii) externally.
Find the position vector of the midpoint of the vector joining the points P(2,3,4) and Q(4, 1, -2).
Show that the points A, B and C with position vectors,
respectively from the vertices of a right angled triangle.
Let O is the origin, then according to question,
Hence ∆ABC is a right angled triangle,
or point A, B and C are the vertices of a right angled triangle.