If `bar(a).bar(b) = bar(a).bar(c )` and `bar(a) xx bar(b) = bar(a) xx bar(c ), bar(a) != 0`, then show that `bar(b) = bar(c )`.

[bar(a)xx bar(b)" "bar(a)xx bar( c )" "bar(d)] = …………….

Let bar(a),bar(b) be two non-collinear unit vectors, if bar(alpha) = bar(a) -(bar(a).bar(b))bar(b) and bar(beta) = bar(a) xx bar(b), then show that |bar(beta)| = |bar(alpha)| .

If bar(a)bar(b)bar(c ) and bar(d) are vectors such that bar(a) xx bar(b) = bar(c ) xx bar(d) and bar(a) xx bar(c ) = bar(b)xxbar(d) . Then show that the vectors bar(a) - bar(d) and bar(b) -bar(c ) are parallel.

If bar(a)+bar(b)+bar(c)=bar(0) then bar(a)timesbar(b)=

Let bar(a), bar(b), bar(c ) be unit vectors, suppose that bar(a). bar(b) = bar(a). bar(c )= 0 and the angle between bar(b) and bar(c ) is pi//6 then show that bar(a)= +-2 (bar(b) xx bar( c))

If 4bar(a)+5bar(b)+9bar(c)=bar(0) then (bar(a)xxbar(b))xx[(bar(b)xxbar(c))xx(bar(c)xxbar(a))]=