`(bar a xx bar b)^2 + (bar a * bar b)^2 = 144` and `|bar a| = 4, |bar b| = `

If |bar(a)xx bar(b)|^(2)+|bar(a).bar(b)|^(2)=144 and |bar(a)|=4 , then |bar(b)| is equal to ……………….

If bar r=l(bar b xx bar c)+m(bar c xx bar a)+n(bar a xx bar b) and [bar a bar b bar c]=2 , then l+m+n is equal to

If bar a = 2 bar I + bar j - bar k, bar b = - bari + 2 bar j - 4 bar k and bar c = bar I + bar j + bar k , then find ( bar a xx bar b) cdot (bar b xx bar c) .

bar a, bar b, bar c are three vectros, then prove that: (bar a xx bar b) xx bar c = (bar a. bar c) bar b-(bar b. bar c) bar a.

(d) answer ANY one question :1. bar a, bar b and bar c be three vectors such that bar a +bar b+ bar c =0 and |bar a|=1, |bar b|=4,|bar c |=2 . Evlautae bar a.bar b + bar b.bar c+bar c.bar a .

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+2 bar b+3bar c=bar 0 then bar axxbar b+bar b xx bar c+bar cxx bara = lambda (bar b xx bar c) ,where lambda=

Compute bar(a) xx (bar(b) + bar(c )) + bar(b) xx (bar(c ) +bar(a)) + bar(c ) xx (bar(a)+bar(b))

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 ) .