Home
Class 11
MATHS
Let a,b,c be three non-zero vectors such...

Let a,b,c be three non-zero vectors such that `a+b+c=0`, then `λb×a+b×c+c×a=0, where λ` is

Text Solution

AI Generated Solution

To solve the problem, we start with the given condition that \( a + b + c = 0 \). This implies that \( c = - (a + b) \). We need to find the value of \( \lambda \) such that: \[ \lambda (b \times a) + (b \times c) + (c \times a) = 0 \] ...
Doubtnut Promotions Banner Mobile Dark
|

Topper's Solved these Questions

  • DIFFERENT PRODUCTS OF VECTORS AND THEIR GEOMETRICAL APPLICATIONS

    CENGAGE ENGLISH|Exercise Exercise 2.3|18 Videos
  • DIFFERENT PRODUCTS OF VECTORS AND THEIR GEOMETRICAL APPLICATIONS

    CENGAGE ENGLISH|Exercise single correct answer type|28 Videos
  • DIFFERENT PRODUCTS OF VECTORS AND THEIR GEOMETRICAL APPLICATIONS

    CENGAGE ENGLISH|Exercise Exercise 2.1|18 Videos
  • CONIC SECTIONS

    CENGAGE ENGLISH|Exercise All Questions|1344 Videos
  • LIMITS AND DERIVATIVES

    CENGAGE ENGLISH|Exercise All Questions|691 Videos

Similar Questions

Explore conceptually related problems

Let vec a , vec b and vec c be three non-zero vectors such that vec a+ vec b+ vec c=0 and lambda vec bxx vec a+ vec bxx vec c+ vec cxx vec a=0, then find the value of lambda

Let vec(a) , vec(b) and vec(c) be three non-zero vectors such that no two of them are collinear and (vec(a)×vec(b))×vec(c)=1/3|vec(b)||vec(c)|vec(a) . If theta is the angle between vectors vec(b) and vec(c) , then the value of sintheta is:

If a,b and c are three non-zero vectors such that no two of these are collinear. If the vector a+2b is collinear with c and b+3c is collinear with a( lamda being some non-zero scalar), then a+2b+6c is equal to

Let a,b and c be three unit vectors such that 3a+4b+5c=0 . Then which of the following statements is true?

Let a, b, c be three vectors such that each of them are non-collinear, a+b and b+c are collinear with c and a respectively and a+b+c=k. Then (|k|, |k|) lies on

Let veca,vecb,vecc be three non zero vectors which are pairwise non colinear. If a + 3b is collinear with c and b+2c is collinear with a, then a + 3b + 6c is equal to (A) a+c (B) a (C) c (D) 0

a, b, c are three vectors, such that a+b+c=0 |a|=1, |b|=2, |c|=3, then a*b+b*c+c*a is equal to

Let vec a , vec b , vec c , be three non-zero vectors. If vec a .(vec bxx vec c)=0 and vec b and vec c are not parallel, then prove that vec a=lambda vec b+mu vec c ,w h e r elambda are some scalars dot

Let a and b be given non-zero and non-collinear vectors, such that ctimesa=b-c . Express c in terms for a, b and aXb.

If a,b,c be non-zero vectors such that a is perpendicular to b and c and |a|=1,|b|=2,|c|=1,b*c=1 and there is a non-zero vector d coplanar with a+b and 2b-c and d*a=1 , then minimum value of |d| is