which of
the following statements are correct:
(a) 
and 
must each
be a null vector,
(b) The magnitude of 
equals
the magnitude of 
(c) The magnitude of a can never
be greater than the sum of the magnitudes of 
and 
(d) 
must lie
in the plane of 
and
if a and
are not collinear, and in the line of and , they are
collinear ?
Answer:
(a) 
and
need not
each be a null vector. The resultant of four non-zero vectors can be a null vector
in many ways e.g., the resultant of any three vectors may be equal to the
magnitude of fourth vector but has the opposite direction. Hence the statement and must each
be a null vector, is not correct.
(b) Because 
hence 
i.e., the
magnitude of 
is equal
to the magnitude 
but
their directions are opposite. Hence the given statement is correct.
(c) Because, or 
.
Hence, magnitude of vector a is
equal to magnitude vector 
.
The sum of the magnitudes of vectors 
and
may be
greater than or equal to that of vector 
(or
vector 
). Hence
the statement that the magnitude of a can never be greater than the sum of the
magnitudes of and
is
correct.
(d) Because hence 
.
The resultant sum of three vectors 
and can be zero
only if 
is in
plane of and . In case and are
collinear, must be
in line of and . Hence
the given statement is correct.
You need to login to perform this action.
You will be redirected in
3 sec
