Statement-I `A=2hat(i)+3hat(j)+6hat(k), B=hat(i)+hat(j)-2hat(k) and C=hat(i)+2hat(j)+hat(k)`, then `|Atimes(Atimes(AtimesB))*C|=243`
Statement-II `|Axx(Axx(AxxB))*C|=|A|^(2)2|[A B C]|`

If a=hat(i)+2hat(j)-2hat(k), b=2hat(i)-hat(j)+hat(k) and c=hat(i)+3hat(j)-hat(k) , then atimes(btimesc) is equal to

If a=2hat(i)+3hat(j)-hat(k), b=-hat(i)+2hat(j)-4hat(k), c=hat(i)+hat(j)+hat(k) , then find the value of (atimesb)*(atimesc) .

Vector vec(A)=hat(i)+hat(j)-2hat(k) and vec(B)=3hat(i)+3hat(j)-6hat(k) are :

Show that the vectors hat(i)-hat(j)-6hat(k),hat(i)-3hat(j)+4hat(k)and2hat(i)-5hat(j)+3hat(k) are coplanar.

If vec(A)=2hat(i)+hat(j)+hat(k) and vec(B)=hat(i)+hat(j)+hat(k) are two vectors, then the unit vector is

Find the angle between vec(A) = hat(i) + 2hat(j) - hat(k) and vec(B) = - hat(i) + hat(j) - 2hat(k)

Show that the points A(-2 hat i+3 hat j+5 hat k), B( hat i+2 hat j+3 hat k) and C(7 hat i- hat k) are collinear.

Examine whether the vectors a=2hat(i)+3hat(j)+2hat(k), b=hat(i)-hat(j)+2hat(k) and c=4hat(i)+2hat(j)+4hat(k) form a left handed or a right handed system.

Statement 1: If vec A=2 hat i+3 hat j+6 hat k , vec B= hat i+ hat j-2 hat ka n d vec C= hat i+2 hat j+ hat k , then | vec Axx( vec Axx( vec Axx vec B))dot vec C|=243. Statement 2: | vec Axx( vec Axx( vec Axx vec B))dot vec C|=| vec A|^2|[ vec A vec B vec C]|dot

Find the altitude of a parallelopiped whose three conterminous edges are verctors A=hat(i)+hat(j)+hat(k), B=2hat(i)+4hat(j)-hat(k) and C=hat(i)+hat(j)+3hat(k) with A and B as the sides of the base of the parallelopiped.