If the vectors `ahat(i)+ahat(j)+chat(k),hat(i)+hat(j)`andchat(i)+chat(j)+bhat(k)` are coplanar, prove that c is the geometric mean of a and b .

If the vectors vecalpha=a hat i+a hat j+c hat k , vecbeta= hat i+ hat ka n d vecgamma=c hat i+c hat j+b hat k are coplanar, then prove that c is the geometric mean of aa n dbdot

Show that the vectors are coplanar 2hat(i)+3hat(j)+hat(k),hat(i)-hat(j),7hat(i)+3hat(j)+2 hat(k)

Let a,b,c be distinct non- negative numbers . If the vectors ahat(i) + ahat(j) + chat(k) , hat(i) + hat(k) " and " chat(i) + c hat(j) + bhat(k) lie in a plane then c is

Determine whether the three vectors 2hat(i)+3hat(j)+hat(k),hat(i)-2hat(j)+2hat(k)and3hat(i)+hat(j)+3hat(k) are coplanar.

Show that the vectors are coplanar hat(i)-2hat(j)+3hat(k),-2hat(i)+3hat(j)-4hat(k),-hat(j)+2hat(k)

If the vector ahat(i)+hat(j)+hat(k), hat(i)+bhat(j)+hat(k)andhat(i)+hat(j)+chat(k)(anebnecne1) are coplanar, then (1)/(1-a)+(1)/(1-b)+(1)/(1-c)=

A vector perpendicular to both hat(i) + hat(j) + hat(k) and 2hat(i) + hat(j) + 3hat(k) is,

Let alpha in R and the three vectors a=alpha hat(i) + hat(j) +3hat(k) , b=2hat(i) +hat(j) -alpha hat(k) " and " c= alpha hat(i) -2hat(j) +3hat(k) . Then the set S={alpha: a,b " and c are coplanar"}

Dot product of a vector with vector 3hat(i)-5hat(k),2hat(i)+7hat(j)andhat(i)+hat(j)+hat(k) are respectively -1,6 and 5. Find the vector.