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If
, then what can be concluded about the vector
?
It is given that.
Hence, vectorsatisfying
can be any vector.
Find the angle between two vectors
and
with magnitudes
and 2, respectively having
.
It is given that,
Now, we know that
.
Hence, the angle between the given vectors andis
.
Find the angle between the vectors
The given vectors are
.
Also, we know that
.
Find the projection of the vector
on the vector
.
Let
and
.
Now, projection of vector
on
is given by,
Hence, the projection of vector onis 0.
Find the projection of the vector
on the vector
.
Let
and
.
Now, projection of vector
on
is given by,
Show that each of the given three vectors is a unit vector:
Also, show that they are mutually perpendicular to each other.
Thus, each of the given three vectors is a unit vector.
Hence, the given three vectors are mutually perpendicular to each other.
Find the magnitude of two vectors
, having the same magnitude and such that the angle between them is 60° and their scalar product is
.
Let θ be the angle between the vectors
It is given that
We know that
.
If
are such that
is perpendicular to
, then find the value of λ.
Hence, the required value of λ is 8.
Show that 
is perpendicular to
, for any two nonzero vectors
Hence, andare perpendicular to each other.
If 
are unit vectors such that 
, find the value of 
.
It is given that .
From (1), (2) and (3),
If either vector
, then
. But the converse need not be true. Justify your answer with an example.
We now observe that:
Hence, the converse of the given statement need not be true.
If the vertices A, B, C of a triangle ABC are (1, 2, 3), (–1, 0, 0), (0, 1, 2), respectively, then find ∠ABC. [∠ABC is the angle between the vectors
and
]
The vertices of ΔABC are given as A (1, 2, 3), B (–1, 0, 0), and C (0, 1, 2).
Also, it is given that ∠ABC is the angle between the vectorsand.
Now, it is known that:
.
Show that the points A (1, 2, 7), B (2, 6, 3) and C (3, 10, –1) are collinear.
The given points are A (1, 2, 7), B (2, 6, 3), and C (3, 10, –1).
Hence, the given points A, B, and C are collinear.
Show that the vectors
form the vertices of a right angled triangle.
Let vectors be position vectors of points A, B, and C respectively.
Now, vectors
represent the sides of ΔABC.
Hence, ΔABC is a right-angled triangle.
If
is a nonzero vector of magnitude ‘a’ and λ a nonzero scalar, then λis unit vector if
(A) λ = 1 (B) λ = –1 (C) 
(D) 
Vector
is a unit vector if
.
Hence, vectoris a unit vector if.
The correct answer is D.
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and
, if
. 
. 
, if for a unit vector
. 
