Find `[bar(a)bar(b)bar(c)]` where :
(1) `bar(a)=2hat(i)+hat(j)-hat(k),bar(b)=3hat(i)-hat(j)-hat(k),hat(c)=hat(j)+3hat(k)`
(2) `bar(a)=7hat(i)-hat(j)+2hat(k),bar(b)=hat(i)+3hat(j)-hat(k),bar(c)=4hat(i)+5hat(k)`.

Find bar(a). bar(b) xx bar(c) , if bar(a) = 3 hat(i) - hat(j) + 4 hat(k), bar(b) = 2hat(i) + 3 hat(j) - hat(k), bar(c) = - 5 hat(i) + 2 hat(j) + 3 hat(k)

If bar(a)=3hat(i)-2hat(j)+7hat(k),bar(b)=5hat(i)+hat(j)-2hat(k)andbar(c)=hat(i)+hat(j)-hat(k) , then find bar(a)*(bar(b)xxbar(c)) .

Express bar(p) as a linear combination of bar(a),bar(b)andbar(c) , where bar(p)=hat(i)+4hat(j)-4hat(k),bar(a)=2hat(i)-hat(j)+3hat(k),bar(b)=hat(i)-2hat(j)+4hat(k),bar(c)=-hat(i)+3hat(j)-5hat(k) .

Find the volume of the parallelopiped whose coterminus edges are : (1) 3hat(i)+5hat(k),4hat(i)+2hat(j)-3hat(k),3hat(i)+hat(j)+4hat(k) (2) bar(a)=hat(i)+hat(j),bar(b)=hat(j)+hat(k),bar(c)=hat(k)+hat(i) (3) 2hat(i)+5hat(j)-4hat(k),5hat(i)+7hat(j)+5hat(k),4hat(i)+5hat(j)-2hat(k) .

If bar(a)=hat(i)+hat(j)+hat(k),bar(b)=2hat(i)+qhat(j)+hat(k),hat(c)=hat(i)-hat(j)+4hat(k)andbar(a)*(bar(b)xxbar(c))=1 , then find the value of q.

If bar(P)=hat i+hat j+hat k,bar(Q)=2hat i-hat j-hat k , then bar(P)-bar(Q) is