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Given that veca,vecb,vecp,vecq are four...

Given that `veca,vecb,vecp,vecq` are four vectors such that `veca + vecb= mu vecp,vecb.vecq=0 and (vecb)^(2) ` where `mu` is a sclar. Then `|(veca.vecq) vecp-(vecp.vecq)veca|` is equal to

A

`2|vecpvecq|`

B

`(1//2)|vecp.vecq|`

C

`|vecpxxvecq|`

D

`|vecp.vecq|`

Text Solution

Verified by Experts

The correct Answer is:
d
`veca + vecb = mu vecp " " vecb.vecq =0, |vecb|^92) =1`
`veca + vecb = muvecp`
` Rightarrow (veca + vecb) xx veca = mu vecp xx veca, vecb xx veca= muvecp xx veca`
` Rightarrow vecq xx ( vecb xx veca) = muvecq xx ( vecp xx veca) `
` Rightarrow (vecq .veca) vecb - ( vecq .vecb) veca = muvecq xx (vecp xx veca)`
`Rightarrow (vecq. veca) vecb = muvecq xx (vecp xx veca)`
`veca + vecb = mu vecp`
` Rightarrow vecq. (veca + vecb) = mu vecq. vecp`
` Rightarrow vecq. veca + vecq . vecb = muvecp .vecq`
` Rightarrow mu = (vecq.veca)/(vecp.vecq) `
`Rightarrow (vecq. veca)vecb = (vecq.veca)/(vecp.vecq) [(vecq.veca) .vecp - (vecq.vecp) veca]`
` Rightarrow | (vecq.veca) vecp -(vecq.vecp) veca| = |vecp.vecq|vecb| = |(vecp.vecq)| . |vecb|`
` Rightarrow |(vecq.veca) vecp.- (vecq.vecp) ]veca| = |vecp.vecq|`
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CENGAGE-DIFFERENT PRODUCTS OF VECTORS AND THEIR GEOMETRICAL APPLICATIONS -Exercise
  1. If vecr and vecs are non-zero constant vectors and the scalar b is cho...

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  2. veca and vecb are two unit vectors that are mutually perpendicular. A...

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  3. Given that veca,vecb,vecp,vecq are four vectors such that veca + vecb...

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  4. The position vectors of the vertices A, B and C of a triangle are thre...

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  5. If a is real constant A ,Ba n dC are variable angles and sqrt(a^2-4)ta...

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  6. The vertex A of triangle ABC is on the line vecr=hati+hatj+lambda hatk...

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  7. A non-zero vecto veca is such tha its projections along vectors (hati ...

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  8. Position vector hat k is rotated about the origin by angle 135^0 i...

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  9. ln a quadrilateral ABCD, vec(AC) is the bisector of the (vec(AB) ^^ v...

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  10. In fig. 2.33 AB, DE and GF are parallel to each other and AD, BG and E...

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  11. Vectors hata in the plane of vecb = 2 hati +hatj and vecc = hati-hatj ...

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  12. Let A B C D be a tetrahedron such that the edges A B ,A Ca n dA D a...

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  13. Let vecf(t)=[t] hat i+(t-[t]) hat j+[t+1] hat k , w h e r e[dot] deno...

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  14. If veca is parallel to vecb xx vecc, then (veca xx vecb) .(veca xx vec...

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  15. The three vectors hat i+hat j,hat j+hat k, hat k+hat i taken two at a ...

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  16. If vecd=vecaxxvecb+vecbxxvecc+veccxxveca is a on zero vector and |(vec...

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  17. If |veca|=2 and |vecb|=3 and veca.vecb=0, " then " (vecaxx(vecaxx(veca...

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  18. If two diagonals of one of its faces are 6hati + 6 hatk and 4 hatj + ...

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  19. The volume of a tetrahedron fomed by the coterminus edges veca , vecb ...

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  20. If veca ,vecb and vecc are three mutually orthogonal unit vectors , th...

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