If `[bara+2bar b 2bar b+bar c 5bar c+bara]=k[bar a bar b bar c]`

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=

If bar a=hat i +hat j+ hat k, bar b=hat i-hat j +hat k, bar c=hat i +2hat j-hat k then the value of |[bar a.bar a, bar a.bar b, bar a.bar c],[bar b.bar a,bar b.bar b, bar b.bar c],[bar c.bar a,bar c.bar b,bar c.barc]|

If bar(a),bar(b)andbar(c) are any three vectors, prove that (1) [bar(a)+bar(b) bar(b)+bar(c) bar(c)+bar(a)]=2[bar(a)bar(b)bar(c)] (2) [bar(a) bar(b)+bar(c) bar(a)+bar(b)+bar(c)]=0

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.

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) .

(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) = 2bar(i) + 3bar(j) + 4bar(k), bar(b) = bar(i) + bar(j) -bar(k), bar(c ) = bar(i) - bar(j) + bar(k) , compute bar(a)x(bar(b)xbar(c )) and verify that it is perpendicular to bar(a) .

If bar(a),bar(b),bar(c) are any three vectors, prove that (1) [bar(a)+bar(b)" "bar(a)+bar(c)" "bar(b)]=[bar(a)" "bar(c)" "bar(b)] (2) [bar(a)-bar(b)" "bar(b)-bar(c)" "bar(c)-bar(a)]=0 .

If bar(a)= 2bar(i) - 3bar(j) + 5bar(k), bar(b)= - bar(i) + 4bar(j)+ 2bar(k) then find (bar(a) + bar(b)) xx (bar(a) - bar(b)) and unit vector perpendicular to both bar(a) + bar(b) " & " bar(a)- bar(b) .

If |bar(a)|=|bar(b)|=|bar(c)|=2 and bar(a).bar(b)=bar(b).bar(c)=bar(c).bar(a)=2 then [bar(a) bar(b) bar(c)] equal to