यदि `vec(a)=hat(i)+hat(j)+hat(k),vec(b)=2hat(i)-hat(j)+3hat(k)" और "vec(c)=hat(i)-2hat(j)+hat(k)` तो निम्नलिखित ज्ञात करे
`vec(p)" जो "vec(a)" और "vec(b)` दोनों पर लंब है एवं `vec(p).vec(c)=15`

If vec(a)=2hat(i)+3hat(j)+hat(k), vec(b)=hat(i)-2hat(j)+hat(k) and vec(c )=-3hat(i)+hat(j)+2hat(k) , find [vec(a)vec(b)vec(c )] .

If vec(a)=(2hat(i)-hat(j)+hat(k)), vec(b)=(hat(i)-3hat(j)-5hat(k)) and vec(c)=(3hat(i)-4hat(j)-hat(k)) , find [vec(a)vec(b)vec(c)] and interpret the result.

If vec(a)=7hat(i)-2hat(j)+3hat(k), vec(b)=hat(i)-hat(j)+2hat(k), vec(c )=2hat(i)+8hat(j) , then find vec(a).(vec(b)xx vec(c )) and (vec(b)xx vec(c )).vec(a) .

If vec(a)=hat(i)+hat(j)+hat(k), vec(b)=2hat(i)-hat(j)+3hat(k) " and " vec(c)=hat(i)-2hat(j)+hat(k) find a unit vector in a direction parallel to vector (2vec(a)-vec(b)+3vec(c)) .

If vec (alpha ) = - hat (i) + 2 hat (j) + hat (k) , vec(b) = 3 hat(i) + hat (j) + 2 hat (k) and vec(c ) = 2 hat (i) + hat (j) + 3 hat (k) , find [ vec(c ) vec(a) vec(b)]

If vec(a) = hat (i) + hat (j) - hat (k) , vec (b) = 2 hat (i) - 2 hat (j) + hat (k) and vec(c ) = 3 hat (i) + 2 hat (j) - 2 hat (k) show that , vec (a). (vec(b)+vec(c)) = vec (a).vec(b) + vec (a).vec(c )

Find [vec(a)vec(b)vec(c )] if vec(a)=vec(i)-2hat(j)+3hat(k), vec(b)=2hat(i)-3hat(j)+hat(k) and vec(c )=3hat(i)+hat(j)-2hat(k) .