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The vector perpendicular to the vectors 4hat(i)-hat(j)+3hat(k) and -2hat(i)+hat(j)-2k whose magnitude is 9, is |
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Answer» `3HAT(i)+6hat(j)-6hat(k)` and `c = x hati + y hatj +z hatk` Given, `a*c=0` i.e., ` 4x-y+3z=-0""…(i)` and `b*c=0` i.e, `x^(2)+y^(2)+z^(2)=0""…(ii)` Also, `|c|=9` i.e.,` x^(2)+y^(2)+z^(2)=81""...(iii)` Now, from Eqs. (i) and (ii), we get `2x+z=0impliesz=-2x` On putting this value in Eq. (ii) by 3 and then adding, we get `({:(8x-2y+6z=0),(-6x+3y-6z=0):})/(2x+y=0impliesy=-2x)` On putting this value in Eq. (iv) we get `5x^(2)+4x^(2)=81` `=?9x^(2)=81impliesx^(2)=9` `impliesx = pm 3` `therefore y= pm 6 and z = pm 6` `therefore` REQUIRED vector, `c=x hati+y hatj +z hatk = pm 3 hatipm 6 hatj pm 6 hatk=3 hati-6 hatj - 6 hatkor -3 hati+6 hatj+6 hatk` |
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