Home
Class 12
MATHS
Let a ,b ,c be distinct non-negative num...

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.

Promotional Banner

Similar Questions

Explore conceptually related problems

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?

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)+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 .

The vectors 3 hat i- hat j +2 hat k', 2 hat i+hat j + 3 hat k and hat i + lambda hat j - hat k are coplaner if value of lambda is (A) -2 (B) 0 (C) 2 (D) any real number

If vec a = hat i + hat j, vec b = hat i + hat k, vec c = hat k + hat i, a unit vector parallel to vec a + vec b + vec c

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-3 hat k) are collinear.

If |a a^2 1+ahat3bb^2 1+b^3cc^2 1+c^3|=0 and the vectors vec A= hat i+a hat j+a^2 hat k , vec B= hat i+b hat j+b^2 hat k , vec C= hat i+c hat j+c^2 hat k are non-coplanar, then prove that a b c=-1 .

If vec a= hat i+ hat j+ hat k , vec b=2 hat i- hat j+3 hat k a n d vec c= hat i-2 hat j+ hat k find a unit vector parallel to 2 vec a- vec b+3 vec cdot