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

If bar(a) = bar(i) - bar(j)-bar(k), bar(b) = 2bar(i) - 3bar(j) + bar(k) then find the projection vector of bar(b) on bar(a) and its magnitude.

If bar(a) = bar(i) + bar(j)+bar(k), bar(b) = 2bar(i) + 3bar(j) + bar(k) then find the projection vector of bar(b) on bar(a) and its magnitude.

If bar(a)=bar(i)-2bar(j)+bar(k), bar(b)=2bar(i)+bar(j)+bar(k), bar(c ) = bar(i) + 2bar(j)-bar(k) , then find bar(a) xx (bar(b) xx bar(c )) and |(bar(a)xxbar(b))xxbar(c )| .

If bar(a) = 2bar(i) - bar(j) + bar(k), and bar(b) = bar(i) - 3bar(j) - 5bar(k) then find |bar(a) xx bar(b)| .

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) = 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)= 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) .