Home
Class 12
MATHS
Let vecA , vecB and vecC be vectors of l...

Let `vecA , vecB and vecC` be vectors of legth , 3,4and 5 respectively. Let `vecA` be perpendicular to `vecB + vecC, vecB " to " vecC + vecA and vecC " to" vecA + vecB` then the length of vector `vecA + vecB+ vecC` is __________.

Text Solution

Verified by Experts

The correct Answer is:
`5sqrt2`
Given that `|vecA|=3, |vecB|=4, |vecC|=5`
`vecAbot (vecB + vecC) Rightarrow vecA. (vecB +vecC) =0`

`Rightarrow vecA.vecB + vecA.vecC=0`
` vecB bot (vecC +vecA)RightarrowvecB.(vecC+vecA_=0`
`Rightarrow vecB.vecC+vecB.vecA=0`
`vecCbot (vecA+vecB) RightarrowvecC. (vecA+vecB)=0`
` Rightarrow vecC.vecA+vecC.vecdB=0`
Adding (i), (ii) and (iii) we get
`2(vecA.vecBr+vecB.vecC+vecC.vecA)=0`
Now , `|vecA + vecB + vecC|^(2)`
`(vecA + vecB+vecC).(vecA + vecB+vecC)`
`|vecA|^(2)+|vecB|^(2)+|vecC|^(2)`
`+2(vecA.vecB + vecB.vecC+vecC.vecA)`
9+16+25+0
= 50
`|vecA + vecB +vecC|= 5sqrt2`
Promotional Banner

Topper's Solved these Questions

  • DIFFERENT PRODUCTS OF VECTORS AND THEIR GEOMETRICAL APPLICATIONS

    CENGAGE ENGLISH|Exercise True and false|3 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 Subjective type|19 Videos

  • DETERMINANTS

    CENGAGE ENGLISH|Exercise All Questions|264 Videos

  • DIFFERENTIAL EQUATIONS

    CENGAGE ENGLISH|Exercise Matrix Match Type|5 Videos

Similar Questions

Explore conceptually related problems

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

if veca , vecb ,vecc are three vectors such that veca +vecb + vecc = vec0 then

[ veca + vecb vecb + vecc vecc + veca ]=[ veca vecb vecc ] , then

Let vecA, vecB and vecC be unit vectors such that vecA.vecB = vecA.vecC=0 and the angle between vecB and vecC " be" pi//3 . Then vecA = +- 2(vecB xx 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 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 , vecc are unit vectors such that veca+ vecb+ vecc= vec0 find the value of (veca* vecb+ vecb* vecc+ vecc*veca) .

vecA, vecB and vecC are vectors each having a unit magneitude. If vecA + vecB+vecC=0 , then vecA. vecB+vecB.vecC+ vecC.vecA will be:

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

If |veca|=4, |vecb|=4 and |vecc|=5 such that veca bot vecb + vecc, vecb bot (vecc + veca) and vecc bot (veca + vecb) , then |veca + vecb + vecc| is: