Show that the points whose position vectors are `-2hat(i)+3hat(j)+5hat(k),hat(i)+2hat(j)+3hat(k)` and `7hat(i)-hat(k)` are collinear.

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

Statemen-I The locus of a point which is equidistant from the point whose position vectors are 3hat(i)-2hat(j)+5hat(k) and (hat(i)+2hat(j)-hat(k)) is r(hat(i)-2hat(j)+3hat(k))=8. Statement-II The locus of a point which is equidistant from the points whose position vectors are a and b is |r-(a+b)/(2)|*(a-b)=0 .

The volume of the tetrahedron whose vertices are the points with position vectors hat(i)+hat(j)+hat(k), -hat(i)-3hat(j)+7hat(k), hat(i)+2hat(j)-7hat(k) and 3hat(i)-4hat(j)+lambdahat(k) is 22, then the digit at unit place of lambda is.

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.

Find lambda if the vectors hat(i) - hat(j) + hat(k) , 3 hat (i) + hat(j) + 2 hat(k) and lambda hat(j) - 3 hat(k) are coplanar

Show that the points A,B and C whose position vectors are repectively 2 hat i+ hat j- hat k , 3 hat i- 2 hat j+ hat k and hat i+ 4 hat j- 3 hat k are collinear.

Prove that the points whose position vectors are hat i - hat j+ hat k , 2 hat i+ 3 hat j+ hat k , hat i+ 2 hat j+ 3 hat k , -2 hat j+ 3 hat k lie in the same plane.

Find the angle between the vectors hat(i)+3hat(j)+7hat(k) and 7hat(i)-hat(j)+8hat(k) .

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

Prove that the points whose position vectors are 6 hat i - 7 hat j, 16 hat i -29 hat j -4 hat k , 3 hat j -6 hat k and 2 hat i+5 hat j +10 hat k are coplanar.