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Let a=hati+2hatj+hatk, b=hati-hatj+hatk and c=hati+hatj-hatk. A vector in the plane a and b whose projection on c is (1)/(sqrt3), is |
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Answer» `HATI+hatj-2hatk` `thereforer = ( hati + 2 hatj + HATK ) + lambda(hati-hatj+hatk)` `=(1+lambda)hati + (2 -lambda)hatj + (1+lambda)hatk` PROJECTION of r on `c=(r*c)/(|c|)` `rArr ([(1+lambda)hati+(2-lambda)hatj+(1+lambda)hatk]*(hati+hatj-hatk))/(sqrt((1)^(2)+(1)^(2)+(-1)^(2)))=|(1)/(sqrt(3))|` `rArr (1+lambda + 2 -lambda - 1-lambda)/(sqrt(3))=|(1)/(sqrt(3))|` `rArr2-lambda = pm 1 rArr lambda 1,3 ` `thereforer = 2 hati +hatj + 2 hatk , 4 hati -hatj + 4 hatk` |
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