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For given vectors, 
and 
, find the unit vector in the direction of the vector 
The given vectors are and.
Hence, the unit vector in the direction of 
is
(a→+b→)???a→+b→???=iˆ+kˆ2√=12√i?+12√k?.a→+b→a→+b→=i^+k^2=12i?+12k?.
Compute the magnitude of the following vectors:
The given vectors are:
Write two different vectors having same magnitude.
Hence, 
are two different vectors having the same magnitude. The vectors are different because they have different directions.
Write two different vectors having same direction.
The direction cosines of 
are the same. Hence, the two vectors have the same direction.
Find the values of x and y so that the vectors 
are equal
The two vectors will be equal if their corresponding components are equal.
Hence, the required values of x and y are 2 and 3 respectively.
Find the scalar and vector components of the vector with initial point (2, 1) and terminal point (–5, 7).
The vector with the initial point P (2, 1) and terminal point Q (–5, 7) can be given by,
Hence, the required scalar components are –7 and 6 while the vector components are 
Find the unit vector in the direction of the vector
.
The unit vector 
in the direction of vector is given by
.
Find the unit vector in the direction of vector
, where P and Q are the points
(1, 2, 3) and (4, 5, 6), respectively.
The given points are P (1, 2, 3) and Q (4, 5, 6).
Hence, the unit vector in the direction of is
.
Find a vector in the direction of vector 
which has magnitude 8 units.
Hence, the vector in the direction of vector which has magnitude 8 units is given by,
Show that the vectors
are collinear.
.
Hence, the given vectors are collinear.
Find the direction cosines of the vector 
Hence, the direction cosines of 
Find the direction cosines of the vector joining the points A (1, 2, –3) and
B (–1, –2, 1) directed from A to B.
The given points are A (1, 2, –3) and B (–1, –2, 1).
Hence, the direction cosines of 
are 
Show that the vector 
is equally inclined to the axes OX, OY, and OZ.
Therefore, the direction cosines of 
Now, let α, β, and γbe the angles formed by 
with the positive directions of x, y, and z axes.
Then, we have
Hence, the given vector is equally inclined to axes OX, OY, and OZ.
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 ration 2:1
(i) internally
(ii) externally
The position vector of point R dividing the line segment joining two points
P and Q in the ratio m: n is given by:
Internally:
Externally:
Position vectors of P and Q are given as:
(i) The position vector of point R which divides the line joining two points P and Q internally in the ratio 2:1 is given by,
(ii) The position vector of point R which divides the line joining two points P and Q externally in the ratio 2:1 is given by,
Find the position vector of the mid point of the vector joining the points P (2, 3, 4) and Q (4, 1, – 2).
The position vector of mid-point R of the vector joining points P (2, 3, 4) and Q (4, 1, – 2) is given by,
Show that the points A, B and C with position vectors,
, 
respectively form the vertices of a right angled triangle.
Position vectors of points A, B, and C are respectively given as:
???AB−→−???2+???CA−→−???2=35+6=41=???BC−→−???2AB→2+CA→2=35+6=41=BC→2
Hence, ABC is a right-angled triangle.
In triangle ABC which of the following is not true:
A. 
B. 
C. 
D. 
On applying the triangle law of addition in the given triangle, we have:
From equations (1) and (3), we have:
Hence, the equation given in alternative C is incorrect.
The correct answer is C.
If 
are two collinear vectors, then which of the following are incorrect:
A. 
, for some scalar λ
B. 
C. the respective components of are proportional
D. both the vectors have same direction, but different magnitudes
If are two collinear vectors, then they are parallel.
Therefore, we have:
(For some scalar λ)
If λ = ±1, then .
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