If `bar(P) = 2i + 4j + 14k ` and `bar(Q) = 4i + 4j + 10k,` find the magnitude of `bar(P) + bar(Q)` .

If bar(p) = xbar(i) + ybar(j) + zbar(k) , find the value of |bar(p) xx bar(k)|^(2)

If bar(a) = 2bar(i) - 3bar(j) + bar(k) and bar(b) = bar(i) + 4bar(j) -2bar(k) , then find (bar(a) + bar(b))xx(bar(a)-bar(b))

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) .

If bar(P)=i+j+2k and bar(Q)=3i-2j+k ,the unit vector perpendicular to both bar(P) and bar(Q) is

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) .