Show that the vectors
` a = 2 hat (i) + 3hat (j) + 6 hat (k) , b = 3 hat (i) - 6 hat (j) + 2 hat (k) ` and ` c= 6 hat (i) + 2 hat (j) - 3 hat (k) ` are mutually perpendicular

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)

In each of the following show that the given vectors are coplanar: vec(a) = hat (i) + hat (j) - 6 hat (k) , vec(b) = hat (i) + 3 hat (j) + 4 hat (k) , vec(c) = 2 hat (i) + 5 hat (j) + 3 hat (k)

a=2hat i+3hat j+6hat k,b=3hat i-6hat j+2hat k and c=6hat i+2hat j-3hat k are mutually perpendicular.

Prove that the vectors A = 2 hati - 3 hat 3 j+hat k and B= hat i+hat j + hat k are mutually perpendicular.

12).Show that the vector hat i+hat j+hat k is equally inclined with the coordinate axes.( 13 show that the vectors vec a=(1)/(7)(2hat i+3hat j+6hat k),vec b=(1)/(7)(3hat i-6hat j+2hat k),vec c=(1)/(7)(6hat i+2hat j-3hat k) are mutually perpendicular unit vectors.

Find the magnitude of the vector (2hat(i) - 3hat(j) - 6hat(k)) + (-hat(i) + hat(j) + 4hat(k)) .

Show that the two vectors vec(A) and vec(B) are parallel , where vec(A) = hat(i) + 2 hat(j) + hat(k) and vec(B) = 3 hat(i) + 6 hat(j) + 3 hat(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.

If 3 hat i + 6 hat j + 2 hat k , hat i - 2 hat j + 3 hat k and 5 hat i + 2 hat j + m hat k are coplanar.