Home
Class 11
MATHS
Let tianglePQR be a triangle . Let veca=...

Let `tianglePQR` 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

`|vecaxxvecvb + veccxxveca|= 48sqrt3`

D

`veca.vecb=-72`

Text Solution

Verified by Experts

The correct Answer is:
a,c,d
`veca + vecb+vecc =0`
`Rightarrow vecb + vecc= -veca`
`Rightarrow |vecb|^(2) +|vecc|^(2) + 2vecb.vecc= |veca|^(2)`
` Rightarrow 48 + |vec|^(2) + 48 = 144 `
` Rightarrow |vecc|^(2)=48`
`|vecc|= 4sqrt3`
` (|vecc|)^(2))/2+|veca|=36`
Further,
`veca+vecb=-vecc`
`Rightarrow |veca|^(2)+|vecb|^(2)+2veca.vecb=|vecc|^(2)`
`Rightarrow 144 + 48 + 2 veca. vecb= 48`
`veca. vecb = -72`
`veca.vecb + vecc=0`
`Rightarrow veca xx vecb +veca xx vecc=0`
`|veca xx vecb +vecc xx veca|`
`2|veca xx vecb|`
`=2 sqrt(a^(2)b^(2)-(veca.vecb)^(2))`
`2sqrt((144)(48)-(72)^(2))=48sqrt3`
Promotional Banner

Topper's Solved these Questions

  • DIFFERENT PRODUCTS OF VECTORS AND THEIR GEOMETRICAL APPLICATIONS

    CENGAGE|Exercise JEE Previous Year (Single Question)|28 Videos

  • CONIC SECTIONS

    CENGAGE|Exercise Solved Examples And Exercises|1316 Videos

  • LIMITS AND DERIVATIVES

    CENGAGE|Exercise Solved Examples And Exercises|320 Videos

Similar Questions

Explore conceptually related problems

Let triangle PQR be a triangle. Let veca = vec(QR) , vecb = vec(RP) and vecc= vec(PQ) . " if " |veca| = 12, |vecb| = 4sqrt3 and vecb , vecc = 24 , then which of the following is ( are ) true ?

Let Delta PQR be a triangle Let veca=bar(QR),vecb=bar(RP)and vecc=bar(PQ)if |veca|=12,|vecb|=4 sqrt(3)and vecb.vecc=24, then which of the following is (are ) true ?

Let veca, vecb ,vecc be unit vetors such that veca + vecb + vecc = vec0 , which one of the following is correct ?

Let vecC=vecA+vecB

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 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 .

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,

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