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
Given four points P1,P2,P3andP4 on the coordinate plane with origin O which satisfy the condition (OP)n−1+(OP)n+1=23OPn (i) If P1 and P2 lie on the curve xy=1 , then prove that P3 does not lie on the curve (ii) If P1,P2,P3 lie on a circle x2+y2=1, then prove that P4 also lies on this circle.
Let a,bandc be unit vectors such that a+b−c=0. If the area of triangle formed by vectors aandbisA, then what is the value of 4A2?
Statement 1: a=3i+pj+3k and b=2i+3j+qk are parallel vectors if p=9/2andq=2. Statement 2: if a=a1i+a2j+a3kandb=b1i+b2j+b3k are parallel, then b1a1=b2a2=b3a3˙
If xandy are two non-collinear vectors and ABC isa triangle with side lengths a,b,andc satisfying (20a−15b)x+(15b−12c)y+(12c−20a)(×xy)=0, then triangle ABC is a. an acute-angled triangle b. an obtuse-angled triangle c. a right-angled triangle d. an isosceles triangle
Column I, Column II Collinear vectors, p.a Coinitial vectors, q. b Equal vectors, r. c Unlike vectors (same intitial point), s. d
If the vectors c,a=xi^+yj^+zk^andb=j^ are such that a,candb form a right-handed system, then find ⋅
In triangle ABC,∠A=300,H
is the orthocenter and D
is the midpoint of BC.
is produced to T
such that HD=DT
The length AT
is equal to
(d). none of these