Show that the point `A , B` and `C` with position vectors ` vec a` =3` hat i` - 4` hat j` -4` hat k` = 2` hat i` `j` + ` hat k` and ` vec c` = ` hat i` - 3` hat j` - 5` hat k` , respectively from the vertices of a right angled triangle.

Show that the points A,B and C with position vectors,vec a=3hat i-4hat j-4hat kvec b=2hat i-hat j+hat k and vec c=hat i-3hat j-5hat k respectively form the vertices of a right angled triangle.

Show that the points whose position vectors are vec a=4hat i-3hat j+k,vec b=2hat i-4hat j+5k,vec c=hat i-hat j form a right triangle.

Show that the points A,B,C with position vectors 2hat i-hat j+hat k,hat i-3hat j-5hat k and 3hat i-4hat j-4hat k respectively,are the vertices of a right angled triangle.Also,find the remaining angles of the triangle.

Show that the points, A, B and C having position vectors (2hat(i)-hat(j)+hat(k)), (hat(i)-3hat(j)-5hat(k)) and (3hat(i)-4hat(j)-4hat(k)) respectively are the vertices of a rightangled triangle. Also, find the remaining angles of the triangle.

The values of a,for which points A,B,C with position vectors 2hat i-hat j+hat k,hat i-3hat j-5hat k and ahat i3hat j+hat k respectively are the vertices of a right angled triangle with C=(pi)/(2) are

The values of a for which the points A,B, and C with position vectors 2hat i-hat j+hat k,hat i-3hat j-5hat k, and ahat i-3hat j+hat k respectively,are the vertices of a right-angled triangle with C=(pi)/(2) are

Prove that the points hat i-hat j,4hat i-3hat j+hat k and 2hat i-4hat j+5hat k are the vertices of a right angled triangle.

Show that the vectors vec a=3 hat i-2 hat j+ hat k , vec b=3 hat j+5 hat k , vec c=2 hat i+ hat j-4 hat k from a right angled triangle.

If vec a=3hat i-hat j-4hat k,vec b=2hat i+4hat j-3hat k and vec c=hat i+2hat j-widehat k, find |3vec a-2hat b+4hat c|

Find the sine of the angle between the vectors vec A = 3 hat i - 4 hat j + 5 hat k and vec B = hat i - hat j + hat k .