If u^and v^are unit vectors and θis the acute angle between them, then 2u^×3v^is a unit vector for
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The position vectors of PandQ
, respectively. If the distance between them is 7, then find the value of a˙
If a,bandc are three non-zero vectors, no two of which ar collinear, a+2b is collinear with c and b+3c is collinear with a, then find the value of ∣∣a+2b+6c∣∣˙
If a,b,andc are three non-coplanar non-zero vecrtors, then prove that (a.a)b×c+(a.b)c×a+(a.c)a×b=[bca]a
Check whether the three vectors 2i^+2j^+3k^,−3i^+3j^+2k^and3i^+4k^
from a triangle or not
If bandc are two-noncollinear vectors such that a∣∣(b×c), then prove that (a×b).(a×c) is equal to ∣a∣2(bc˙)˙
then find (m,n)˙
Show that (a−b)×(a+b)=2a×b
and given a geometrical interpretation of it.
, then A,BnadC
are (where O
is the origin)
a. coplanar b. collinear c. non-collinear d. none of these