Home
Class 12
MATHS
A, B C and D are four points in a plane ...

A, B C and D are four points in a plane with position vectors, `veca, vecb, vecc and vecd` respectively, such that `(veca-vecd).(vecb-vecc)= (vecb-vecd).(vecc-veca)=0` then point D is the ______ of triangle ABC.

Text Solution

Verified by Experts

The correct Answer is:
orthocenter
Given that `veca, vecb , vecc and vecd` are position vectors of points A,B,C and D, respectively, such that
`(veca - vecd) . (vecb - vecc) = (vecb.vecd) . (vecc- veca) =0`
`Rightarrow vec(DA).vec(CB) = vec(DB).vec(AC) =0`
` Rightarrow vec(DA) bot vec(CB) and vec(DB) bot vec(AC)`
Clerly, D is the orthocentre of `triangleABC`
Promotional Banner

Topper's Solved these Questions

  • DIFFERENT PRODUCTS OF VECTORS AND THEIR GEOMETRICAL APPLICATIONS

    CENGAGE PUBLICATION|Exercise True and false|3 Videos

  • DIFFERENT PRODUCTS OF VECTORS AND THEIR GEOMETRICAL APPLICATIONS

    CENGAGE PUBLICATION|Exercise single correct answer type|28 Videos

  • DIFFERENT PRODUCTS OF VECTORS AND THEIR GEOMETRICAL APPLICATIONS

    CENGAGE PUBLICATION|Exercise Subjective type|19 Videos

  • DETERMINANTS

    CENGAGE PUBLICATION|Exercise All Questions|262 Videos

  • DIFFERENTIAL EQUATIONS

    CENGAGE PUBLICATION|Exercise All Questions|578 Videos

Similar Questions

Explore conceptually related problems

If veca, vecb, vecc and vecd are unit vectors such that (vecaxx vecb).(veccxxvecd)=1 and veca.vecc=1/2 then

If veca, vecb, vecc are vectors such that |vecb|=|vecc| then {(veca+vecb)xx(veca+vecc)}xx(vecbxxvecc).(vecb+vecc)=

for any three vectors, veca, vecb and vecc , (veca-vecb) . (vecb -vecc) xx (vecc -veca) =

If [ veca vecbvecc]=2 , then find the value of [(veca+2vecb-vecc) (veca - vecb) (veca - vecb-vecc)]

For any four vectors, prove that ( veca × vecb )×( vecc × vecd )=[ veca vecc vecd ] vecb −[ vecb vecc vecd ] veca

veca,vecb and vecc are three unit vectors . Show that, |veca-vecb|^2+|vecb-vecc|^2+|vecc-veca|^2le9 .

If veca,vecbandvecc are unit vectors such that veca+vecb+vecc=0 , then the value of veca.vecb+vecb.vecc+vecc.veca is

If veca,vecbandvecc are unit vectors such that veca+vecb+vecc=3 , then the value of veca.vecb+vecb.vecc+vecc.veca is

Prove that [veca+vecb vecb+vecc vecc+veca]=2[veca vecb vecc]