Home
Class 12
MATHS
Let PQR be a triangle . Let veca=overlin...

Let `PQR` be a triangle . Let `veca=overline(QR),vecb = overline(RP) and vecc= overline(PQ).if |veca|=12, |vecb|=4sqrt3and vecb.vecc= 24` then which of the following is (are) true ?

A

`(|vecc|^(2))/(2)-|veca|=12`

B

`(|vecc|^(2))/(2)-|veca|=30`

C

`|vecaxxvecb+veccxxveca|=48sqrt(3)`

D

`veca.vecb=-72`

Text Solution

Verified by Experts

The correct Answer is:
A, C, D
`a., c., d. veca+ vecb + vecc=0 `
` implies vecb+ vecc=-veca`
`implies |vecb|+ |vecc|^(2) +2cevb. vecc= |veca|^(2)`
`implies 48+ |vecc|^(2)+48=144`
`implies |vecc|^(2)=48`
`implies |vecc|= 4sqrt(3)`
`therefore ( |vecc|^(2))/(2) +|veca|=36`
futher ,
`veca+vecb=-vecc``implies |veca|^(2)+|vecb|+2veca.vecb=|vecc|^(2)`
` implies 144+48+2veca. vecb=48`
`:' veca+vecb+vecc=0`
`implies veca+vecb +c=0`
` therefore |vecaxxvecb+veccxxveca|`
`2 |vecaxxvecb|`
`= 2 sqrt(a^(2)b^(2)-(veca.vecb)^(2))`
`= 2sqrt((144)(48)-(72)^(2)= 48sqrt(3)`
Promotional Banner

Topper's Solved these Questions

  • JEE 2019

    CENGAGE ENGLISH|Exercise matching column type|2 Videos

  • JEE 2019

    CENGAGE ENGLISH|Exercise chapter -3 multiple correct answers type|2 Videos

  • JEE 2019

    CENGAGE ENGLISH|Exercise Integer Answer type|2 Videos

  • INVERSE TRIGONOMETRIC FUNCTIONS

    CENGAGE ENGLISH|Exercise Archives (Numerical Value type)|2 Videos

  • LIMITS

    CENGAGE ENGLISH|Exercise Comprehension Type|4 Videos

Similar Questions

Explore conceptually related problems

Let vecC=vecA+vecB

Let veca,vecb,vecc be unit vectors such that veca+vecb+vecc=vec0 . Which of the following is correct?

Let veca and vecb are vectors such that |veca|=2, |vecb|=3 and veca. vecb=4 . If vecc=(3veca xx vecb)-4vecb , then |vecc| is equal to

Let veca , vecb,vecc be three vectors such that veca bot ( vecb + vecc), vecb bot ( vecc + veca) and vecc bot ( veca + vecb) , " if " |veca| =1 , |vecb| =2 , |vecc| =3 , " then " | veca + vecb + vecc| is,

Let veca vecb and vecc be pairwise mutually perpendicular vectors, such that |veca|=1, |vecb|=2, |vecc| = 2 , the find the length of veca +vecb + vecc .

Let veca vecb and vecc be pairwise mutually perpendicular vectors, such that |veca|=1, |vecb|=2, |vecc| = 2 , the find the length of veca +vecb + vecc .

If veca, vecb and vecc are such that [veca \ vecb \ vecc] =1, vecc= lambda (veca xx vecb) , angle between vecc and vecb is 2pi//3 , |veca|=sqrt2, |vecb|=sqrt3 and |vecc|=1/sqrt3 then the angle between veca and vecb is

Let veclamda=veca times (vecb +vecc), vecmu=vecb times (vecc+veca) and vecv=vecc times (veca+vecb) , Then

If |veca|=1,|vecb|=2,|vecc|=3and veca+vecb+vecc=0 the show that veca.vecb+vecb.vecc+vecc.veca=- 7

If veca, vecb, vecc are vectors such that veca.vecb=0 and veca + vecb = vecc then: