Let `a=hat(i)+4hat(j)+2hat(k), b=3hat(i)-2hat(j)+7hat(k) and c=2hat(i)-hat(j)+4hat(k)` Find a vector d which is perpendicular to both a and b and c.d=15.

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

Let vec a= hat i+4 hat j+2 hat k ,\ \ vec b=3 hat i-\ 2 hat j+7 hat k and vec c=2 hat i-\ hat j+4 hat k . Find a vector vec d which is perpendicular to both vec a and vec b and vec c . vec d =15.

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

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.

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) .

Let a=hat(i)+hat(j)+hat(k), b=-hat(i)+hat(j)+hat(k), c=hat(i)-hat(j)+hat(k) and d=hat(i)+hat(j)-hat(k) . Then, the line of intersection of planes one determined by a, b and other determined by c, d is perpendicular to

Statement-I If a=3hat(i)-3hat(j)+hat(k), b=-hat(i)+2hat(j)+hat(k) and c=hat(i)+hat(j)+hat(k) and d=2hat(i)-hat(j) , then there exist real numbers alpha, beta, gamma such that a=alphab+betac+gammad Statement-II a, b, c, d are four vectors in a 3-dimensional space. If b, c, d are non-coplanar, then there exist real numbers alpha, beta, gamma such that a=alphab+betac+gammad.

Show that the vectors 2hat(i)-hat(j)+hat(k) and hat(i)-3hat(j)-5hat(k) are at right angles.

The projection of vec(a)=2hat(i)-hat(j)+hat(k) on vec(b)=hat(i)-2hat(j)+hat(k) is equal to :

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.