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 :

Unit vectors vec(a),vec(b),vec(c ) are coplanar. A unit vector vec(d)

1.	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 :
Answer» `PM(1)/(3)(-HAT(i)-2hat(j)+2hat(k))` `(1)/(3)(2hat(i)+hat(j)-hat(k))` `pm(1)/(3)(-hat(i)+2hat(j)-2hat(k))` `(1)/(3)(-2hat(i)-2hat(j)+ hat(k))` Solution :`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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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 :

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