Question

abcd is a quadrilateral prove that ba vector + bc vector+cr vector+ da bector=2ba vector

Answer 1

BA (vector)+BC (vector)+CD (vector) +DA(vector)
BA(vector)+BA(vector)
REASON:Since BC(vector)+CD(vector)+DA(vector)=BA(vector). Using polygon law of vectors
CONTINUATION OF SOLUTION
Therefore
=2BA(VECTOR)
=RHS
HENCE PROVED
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Answer 2

question is -> ABCD is a quadrilateral. prove that

BA + BC + CD + DA = 2BD

proof : according to triangular vector addition.

BC + CD = BD .........(1)

similarly, applying triangular vector addition for ∆ ABD,

i.e., AD + AB + BD = 0 [as head of each vector is joining by tail of other vector ]

we know, from the basic concept of vector

XY = -YX

so, AD = -DA , AB = -BA

so, -DA - BA + BD = 0 ⇒BD = BA + DA .......(2)

from equations (1) and (2),

2BD = BA + DA + BC + CD

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