Find the unit vector in the direction of sum of vectors and
If find the unit vector in the direction of
Find a unit vector in the direction of , where P and Q have co-ordinates (5, 0, 8) and (3, 3, 2), respectively.
If and are the position vectors of A and B, respectively, find the position vector of a point C in BA produced such that BC = 1.5 BA.
Using vectors, find the value of k such that the points (k, – 10, 3), (1, –1, 3) and (3, 5, 3) are collinear.
A vector is inclined at equal angles to the three axes. If the magnitude of is units, find .
A vector has magnitude 14 and direction ratios 2, 3, –6. Find the direction cosines and components of , given that makes an acute angle with x-axis.
Find a vector of magnitude 6, which is perpendicular to both the vectors and
Find the angle between the vectors and
If , show that . Interpret the result geometrically?
Find the sine of the angle between the vectors and
If A, B, C, D are the points with position vectors respectively, find the projection of along .
Using vectors, find the area of the triangle ABC with vertices A(1, 2, 3), B(2, – 1, 4) and C(4, 5, – 1).
Using vectors, prove that the parallelogram on the same base and between the same parallels are equal in area
Prove that in any triangle ABC, where a, b, c are the magnitudes of the sides opposite to the vertices A, B, C, respectively
If determine the vertices of a triangle, show that gives the vector area of the triangle. Hence deduce the condition that the three points a, b, c are collinear. Also find the unit vector normal to the plane of the triangle.
Show that area of the parallelogram whose diagonals are given by and is Also find the area of the parallelogram whose diagonals are
If find a vector such that and .
The vector in the direction of the vector that has magnitude 9 is
The position vector of the point which divides the join of points and in the ratio 3 : 1 is
The vector having initial and terminal points as (2, 5, 0) and (–3, 7, 4), respectively is
The angle between two vectors and with magnitudes and 4, respectively, and is
Find the value of λ such that the vectors and are orthogonal
The value of λ for which the vectors and are parallel is
The vectors from origin to the points A and B are and respectively, then the area of triangle OAB is
For any vector , the value of is equal to
If and then value of is
The vectors -are and coplanar if
If are unit vectors such that , then the value of is
Projection vector of on is
If are three vectors such that and then value of is
If and –3≤λ≤2, then the range of is
The number of vectors of unit length perpendicular to the vectors and is
Fill in the blanks
The vector bisects the angle between the non-collinear vectors and if ________
If and for some non-zero vector , then the value of -is _________
The vectors are the adjacent sides of a parallelogram. The acute angel between its diagonals is ____________.
The values of k for which and is parallel to holds true are _______.
The value of the expression is ______.
If and then is equal to ________.
If is any non-zero vector, then equals ______.
True and False
If , then necessarily at implies .
Position vector of a point P is a vector whose initial point is origin.
If , then the vectors and are orthogonal.
The formula is valid for non-zero vectors and .
If and are adjacent sides of a rhombus, then .
