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

Let a, b and c b the distinct non-negative numbers. If the vectors a hat(i) + a hat(j) + c hat(k), hat(i) + hat(k), c hat(i) + c hat(j) + b hat(k) lie on a plane, then which one of the following is correct?

If the vectors ahat (i) + a hat (j) + c hat (k) , hat (i) + hat (k) and c hat (i) + c hat (j) + b hat (k) be coplanar, show that c^(2) = ab

Let a, b and c be the distinct non-negative numbers. If the vectors a hat(i)+c hat(k), hat(i)+hat(k), c hat(i) + c hat(j)+bhat(k) lie on a plane, then which one of the following is correct?

If the vectors ahat(i)+ahat(j)+chat(k),hat(i)+hat(k) and chat(i)+chat(j)+bhat(k) are coplanar then show that c^(2)=ab

If the vectors (ahat(i)+a hat(j)+chat(k)), (hat(i)+hat(k)) and (c hat(i)+c hat(j)+b hat(k)) be coplanar, show that c^(2)=ab .

Let a ,b ,c be distinct non-negative numbers and the vectors a hat i+a hat j+c hat k , hat i+ hat k ,c hat i+c hat j+b hat k lie in a plane, and then prove that the quadratic equation a x^2+2c x+b=0 has equal roots.

Let a ,b ,c be distinct non-negative numbers and the vectors a hat i+a hat j+c hat k , hat i+ hat k ,c hat i+c hat j+b hat k lie in a plane, and then prove that the quadratic equation a x^2+2c x+b=0 has equal roots.