If vec(beta) is perpendicular to both vec(alpha) and vec(lambda) where vec(alpha)=hat(k) and vec(lambda)=2hat(i)+3 hat(j)+4 hat(k), then what is vec(beta) equal to ?

If vec(beta) is perpendicular to both vec(alpha) and vec(lambda) where

1.	If vec(beta) is perpendicular to both vec(alpha) and vec(lambda) where vec(alpha)=hat(k) and vec(lambda)=2hat(i)+3 hat(j)+4 hat(k), then what is vec(beta) equal to ?
Answer» `3HAT(i)+2hat(J)` `-3hat(i)+2hat(j)` `2hat(i)-3hat(j)` `-2hat(i)+3hat(j)` Solution :Let `VEC(beta)=a hat(i)+b hat(j)+c hat(k)` Since `vec(beta).vec( ALPHA)=0 and vec(beta).vec(lambda)=0` `:. C=0 and 2a + 3b=0 rArr a = - (3b)/(2)` Hence, `vec(beta)=-(3 b)/(2) vec(i)+b hat(j)=0 rArr -3 hat(i)+2 hat(j)=0`

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If vec(beta) is perpendicular to both vec(alpha) and vec(lambda) where vec(alpha)=hat(k) and vec(lambda)=2hat(i)+3 hat(j)+4 hat(k), then what is vec(beta) equal to ?

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