Unit vectors `vec(a),vec(b),vec(c )` are coplanar. A unit vector `vec(d)` is perpendicular to them. If `(vec(a)xxvec(b))xx(vec(c )xxvec(d))=(1)/(6)i-(
Unit vectors `vec(a),vec(b),vec(c )` are coplanar. A unit vector `vec(d)` is perpendicular to them. If `(vec(a)xxvec(b))xx(vec(c )xxvec(d))=(1)/(6)i-(1)/(3)hat(j)+(1)/(3)hat(k)` and the angle between `vec(a)` and `vec(b)` is `30^(@)`, then `vec(c )` is/are :
A. `pm(1)/(3)(-hat(i)-2hat(j)+2hat(k))`
B. `(1)/(3)(2hat(i)+hat(j)-hat(k))`
C. `pm(1)/(3)(-hat(i)+2hat(j)-2hat(k))`
D. `(1)/(3)(-2hat(i)-2hat(j)+ hat(k))`
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Correct Answer - C
`vec(d)=pm((vec(a) xx vec(b)))/(|vec(a) xx vec(b)|)`
`therefore" "(vec(a)xxvec(b).vec(d))vec(c )-(vec(a)xxvec(b).vec(c ))vec(d)=(1)/(6)hat(i)-(1)/(3)hat(j)+(1)/(3)hat(k)impliespm(1)/(2).vec(c )=(1)/(6)(hat(i)-2hat(j)+2hat(k))`
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