Home
Class 12
MATHS
Applying vectors , show that (a(1)b(1)...

Applying vectors , show that
`(a_(1)b_(1)+a_(2)b_(2)+a_(3)b_(3))^(2)le (a_(1)^(2)+a_(2)^(2)+a_(3)^(2))(b_(1)^(2)+b_(2)^(2)+b_(3)^(2))`

Answer

Step by step text solution for Applying vectors , show that (a_(1)b_(1)+a_(2)b_(2)+a_(3)b_(3))^(2)le (a_(1)^(2)+a_(2)^(2)+a_(3)^(2))(b_(1)^(2)+b_(2)^(2)+b_(3)^(2)) by MATHS experts to help you in doubts & scoring excellent marks in Class 12 exams.

Doubtnut Promotions Banner Mobile Dark
|

Topper's Solved these Questions

  • PRODUCTS OF TWO VECTORS

    CHHAYA PUBLICATION|Exercise Exercise 2B ( Short answer type questions)|20 Videos

  • PRODUCTS OF TWO VECTORS

    CHHAYA PUBLICATION|Exercise Sample Questions for Competitive Examination (Multiple Correct Answers Type )|5 Videos

  • PRODUCTS OF TWO VECTORS

    CHHAYA PUBLICATION|Exercise Exercise 2A ( Short answer type questions)|41 Videos

  • PROBABILITY

    CHHAYA PUBLICATION|Exercise SAMPLE QUESTIONS FOR COMPETITIVE EXAMS|18 Videos

  • PROPERTIES OF TRIANGLE

    CHHAYA PUBLICATION|Exercise Assertion- Reason Type:|2 Videos

Similar Questions

Explore conceptually related problems

If a_(1), a_(2), a_(3),…, a_(2k) are in A.P., prove that a_(1)^(2) - a_(2)^(2) + a_(3)^(2) - a_(4)^(2) +…+a_(2k-1)^(2) - a_(2k)^(2) = (k)/(2k-1)(a_(1)^(2) - a_(2k)^(2)) .

If a_(1), a_(2),…,a_(n) are in G.P., then show that (1)/(a_(1)^(2) - a_(2)^(2)) + (1)/(a_(2)^(2) - a_(3)^(2))+...+ (1)/(a_(n-1)^(2) - a_(n)^(2)) = (r^(2))/((1-r^(2))^(2))[(1)/(a_(n)^(2))-(1)/(a_(1)^(2))]

Knowledge Check

  • If the determinant of the matrix [(a_(1),b_(1),c_(1)),(a_(2),b_(2),c_(2)),(a_(3),b_(3),c_(3))] is denoted by D, then the determinant of the matrix [(a_(1)+3b_(1)-4c_(1),b_(1),4c_(1)),(a_(2)+3b_(2)-4c_(2),b_(2),4c_(2)),(a_(3)+3b_(3)-4c_(3),b_(3),4c_(3))] will be -

    A
    D
    B
    2D
    C
    3D
    D
    4D

  • Statement - I: Equation of bisectors of the angles between the liens x=0 and y=0 are y=+-x Statement - II : Equation of the bisectors of the angles between the lines a_(1)x+b_(1)y+c_(1)=0anda_(2)x+b_(2)y+c_(2)=0 are (a_(1)x+b_(1)y+c_(1))/(sqrt(a_(1)^(2)+b_(1)^(2)))=+-(a_(2)x+b_(2)y+c_(2))/(sqrt(a_(2)^(2)+b_(2)^(2))) (Provided a_(1)b_(2)nea_(2)b_(1)andc_(1),c_(2)gt0)

    A
    Statement -I is true , Statement -II is true and Statement - II is a correct explanation for Statement -I.
    B
    Statement -I is true , Statement -II is true but
    Statement -II is not a correct explanation of Statement -I.
    C
    Statement -I is true , Statement -II is false .
    D
    Statement -I is false, Statement -II is true.

    • Similar Questions

    Explore conceptually related problems

    The asymptotes of the hyperbola (x^(2))/(a_(1)^(2))-(y^(2))/(b_(1)^(2))=1 and (x^(2))/(a_(2)^(2))-(y^(2))/(b_(2)^(2))=1 are perpendicular to each other. Then, (a) a_(1)/a_(2)=b_(1)/b_(2) (b) a_(1)a_(2)=b_(1)b_(2) (c) a_(1)a_(2)+b_(1)b_(2)=0 (d) a_(1)-a_(2)=b_(1)-b_(2)

    If x in R,a_(i),b_(i),c_(i) in R for i=1,2,3 and |{:(a_(1)+b_(1)x,a_(1)x+b_(1),c_(1)),(a_(2)+b_(2)x,a_(2)x+b_(2),c_(2)),(a_(3)+b_(3)x,a_(3)x+b_(3),c_(3)):}|=0 , then which of the following may be true ?

    If the ellipse (x^(2))/(a_(1)^(2))+(y^(2))/(b_(1)^(2))=1(a_(1)^(2)gtb_(1)^(2)) has same eccentricity as that of the ellipse (x^(2))/(a_(2)^(2))+(y^(2))/(b_(2)^(2))=1(a_(2)^(2)gtb_(2)^(2)) prove that a_(1)b_(2) =a_(2)b_(1) .

    Let a_(1),a_(2),a_(3), …, a_(10) be in G.P. with a_(i) gt 0 for i=1, 2, …, 10 and S be te set of pairs (r, k), r, k in N (the set of natural numbers) for which |(log_(e)a_(1)^(r)a_(2)^(k),log_(e)a_(2)^(r)a_(3)^(k),log_(e)a_(3)^(r)a_(4)^(k)),(log_(e)a_(4)^(r)a_(5)^(k),log_(e)a_(5)^(r)a_(6)^(k),log_(e)a_(6)^(r)a_(7)^(k)),(log_(e)a_(7)^(r)a_(8)^(k),log_(e)a_(8)^(r)a_(9)^(k),log_(e)a_(9)^(r)a_(10)^(k))| = 0. Then the number of elements in S is

    Represent the following equations in matrix form: a_(1)x+b_(1)y+c_(1)z=k_(1) a_(2)x+b_(2)y+c_(2)z=k_(2) a_(3)x+b_(3)y+c_(3)z=k_(3)

    If (x+1/x+1)^(6)=a_(0)+(a_(1)x+(b_(1))/(x))+(a_(2)x^(2)+(b_(2))/(x^(2)))+"...."+(a_(6)x^(6)+(b_(6))/(x^(6))) , then

    Home
    Profile