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If vecAxxvecB =vecCxxvecD "and"vecAxxvecC=vecBxxvecD+"while"|vecA|-!=|vecD|,|vecB|!=|vecC|, show (vecA-vecD)that, and (vecB-vecC)are parallel. |
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Answer» Solution :Given, `vecAxxvecB=vecCxxvecD` `vecAxxvecC =vecBxxvecD` Subtracting (2)from (1), we get , `vecAxxvecB-vecAxxvecC=vecCxxvecD -vecBxxvecD` `:. vecAxx(vecB-vecC)` `=(vecC -vecB)xxvecD[:.vecPxx(vecQ+vecR)=vecPxxvecQ+vecPxxvecR]` `:. vecAxx(vecB-vecC)=-(vecB-vecC)xxvecD``:. vecAxx(vecB-vecC)+(vecB-vecC)xxvecD=0 ``:.vecAxx(vecB-vecC)-vecDxx(vecB-vecC)=0` `[:.PxxvecQ=-vecQxxvecP]` `:.(VECA-vecD)xx(vecB-vecC)=0` Now,`|vecA|!=|vecD|"and"|vecB|!=|vecC|` `:. (vecA-vecD)!=0"and" (vecB-vecC)!=0` `(vecA-vecD)"and"(vecB-vecC)` are at an angle `0^(@)`or `(vecA-vecD)"and"(vecB-vecC)` are parallel. `[:. vecPxxvecQ=PQsin THETA "and"P!=0!=Q."hence " sin theta=0]` |
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