1.

The vector perpendicular to the vectors 4hat(i)-hat(j)+3hat(k) and -2hat(i)+hat(j)-2k whose magnitude is 9, is

Answer»

`3HAT(i)+6hat(j)-6hat(k)`
`3hat(i)-6hat(j)+6hat(k)`
`-3hat(i)+6hat(j)+6hat(k)`
None of these

Solution :Let `a =4hati - hatj+3 HATK, b=-2 hati+ hatj-2 hatk`
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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