Lett `alpha, beta and gamma` be distinct real numbers. The points whose position vector's are `alpha hat i + beta hat j+gamma hat k; beta hat i+gamma hat j+alpha hat k and gamma hat i+alpha hat j+beta hat k`

Let alpha, beta and gamma be distinct real numbers. The points with position vectors alpha hat(i) + beta hat(j) + gamma hat(k), beta hat(i) + gamma hat(j) + alpha hat(k) and gamma hat(i) + alpha hat(j) + beta hat(k)

Let alpha, beta, gamma be distinct real numbers. The points with position vectors alpha hati + beta hatj +gamma hat k , beta hati + gamma hatj +alpha hat k , gamma hati +alpha hatj + beta hatk

Let alpha, beta , lambda be distinct real numbers. The points with position vectros alpha hat (i) + beta hat(j) + lambda hat(k), beta hat(i) + lambda hat(j) + alpha hat(k) and lambda hat(i) + alpha hat(j) + beta hat (k)

Show that the points whose position vectors are 5hat i+5hat k,2hat i+hat j+3hat k and -4hat i+3hat j-hat k are collinear

The lines vec r=(hat i+hat j+hat k)alpha+3hat k and vec r=(hat i-2hat j+hat k)beta+3hat k

The angle between the vectors (hat i + hat j + hat k) and ( hat i - hat j -hat k) is

If the four points with positing vectors,-2hat i+hat j+hat k,hat i+hat j+hat k,hat j-hat k and lambdahat j+hat k are coplanar,then lambda is equal to

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 points whose position vectors are as given below are collinear: 2hat i+hat j-hat k,3hat i-2hat j+hat k and hat i+4hat j-3hat k3hat i-2hat j+4hat k,hat i+hat j+hat k and -hat i+4hat j-2hat k

Find a set of vectors reciprocal to the set -hat i+hat j+hat k,hat i-hat j+hat k,hat i+hat j+hat k