Find the projection of the a=2i^+3j^+2k^on the b=i^+2j^+k^.
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Statement 1: If ∣∣a+b∣∣=∣∣a−b∣∣, then a and b are perpendicular to each other. Statement 2: If the diagonal of a parallelogram are equal magnitude, then the parallelogram is a rectangle.
Prove that [a+bb+cc+a]=2[abc]˙
I, Column II
Collinear vectors, p.a
Coinitial vectors, q. b
Equal vectors, r. c
Unlike vectors (same intitial point), s. d
Prove that the four points 6i^−7j^,16i^−19j^−4k^,3j^−6k^and2i^+5j^+105^
form a tetrahedron in space.
If the vectors α=ai^+aj^+ck^,β=i^+k^andγ=ci^+cj^+bk^
are coplanar, then prove that c
is the geometric mean of aandb˙
If ∣a∣=2∣∣b∣∣=5 and ∣∣a×b∣∣=8, then find the value of a.b˙
Four non –zero vectors will always be
a. linearly dependent b. linearly independent
c. either a or b d. none of these
The lines joining the vertices of a tetrahedron to the centroids of opposite faces are concurrent.