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If vecA=(2hati+hatj)"and"vecB=(hati-hatj+5hatk).Find vecAxxvecB, angle between vecA"and"vecB Unit vector perpendicular to vecA"and"vecB. |
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Answer» Solution :`vecAxxvecB=|(veci,vecj,veck),(2.1,0,),(1,-1,5)|=veci(5+0)-vecj(10-0)+veck(-2-1)` `:.vecAxxvecB=5veci-10vecj-3veck, sin theta=|vecAxxvecB|/(AB)` `A = SQRT(2^(2)+1^(2))=sqrt5, B=sqrt(1^(2)+(-1)+5^(2))=sqrt(27)` `|vecAxxvecB|=sqrt(5^(2)+(-10)^(2)+(-3)^(2))=sqrt(25+100+9)=sqrt(134)` `:. sin theta = sqrt(134)/(sqrt5sqrt(27)) :. sin ^(-1)sqrt(134)/sqrt(135)` Let `vecu` be the unit vector perpendicular to `vecA "and" VECB` then `vec u` is unit vector along `vecAxxvecB`. `:. vecu= (vecAxxvecB)/|vecAxxvecB|=(5veci-10vecj-3veck)/sqrt(134)` |
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