`hat(i)-2 hat(j) - 3hat(k)`का परिमाण एवं उसकी दिशा में एकांक सदिश ज्ञात कीजिए |

Show that the vectors are mutually perpendicular hat (i) + 2 hat (j) + hat (k) ,hat (i) + hat (j) - 3 hat (k) and 7 hat (i) - 4 hat (j) + hat (k)

The angle between the lines overset(to)( r)=(4 hat(i) - hat(j) )+ lambda(2 hat(i) + hat(j) - 3hat(k) ) and overset(to) (r )=( hat(i) -hat(j) + 2 hat(k) ) + mu (hat(i) - 3 hat(j) - 2 hat(k) ) is

Find the value of lambda , if the point with position vectors 3hat(i) - 2hat(j) - hat(k), 2hat(i) + 3hat(j) - 4hat(k), -hat(i) + hat(j) + 2hat(k) and 4hat(i) + 5hat(j) + lambda hat(k) are coplanar.

Find ( vec (a) xxvec (b)) and |vec(a) xx vec (b)| ,when (i) vec(a) = hat(i)-hat(j)+ 2hat(k) and vec(b)= 2 hat(i)+3 hat(j)-4hat(k) (ii) vec(a)= 2hat (i)+hat(j)+ 3hat(k) and vec(b)= 3hat(i)+5 hat(j) - 2 hat(k) (iii) vec(a)=hat(i)- 7 hat(j)+ 7hat(k) and vec(b) = 3 hat(i)-2hat(j)+2 hat(k) (iv) vec(a)= 4hat(i)+ hat(j)- 2hat(k) and vec(b) = 3 hat(i)+hat(k) (v) vec(a) = 3 hat(i) + 4 hat(j) and vec(b) = hat(i)+hat(j)+hat(k)

Prove that the four points with position vectors hat(i) + hat(j) + 3hat(k) , hat(i) - 2hat(j) + 2hat(k) and 2hat(i) + 2hat(k) are coplanar.

Calculate the product ((hat i- 2 hat j+ 3 hat k) cross (2 hat i+ hat j- 3 hat k)) * (-3 hat i+ hat j+ 2 hat k ) .