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Question
The unit vector perpendicular to both the vectors →a=→i+→j+→k and →b=2→i−→j+3→k and making an acute angle with the vector →k is
The unit vector perpendicular to both the vectors →a=→i+→j+→k and →b=2→i−→j+3→k and making an acute angle with the vector →k is
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Solution
The correct option is B −1√26(4→i−→j−3→k)
The vector perpendicular to vectors →a and →b is given by →a×→b.
Similarly, the vector perpendicular to each of the vectors given above is (→i+→j+→k)×(2→i−→j+3→k)=∣∣
∣
∣∣→i→j→k1112−13∣∣
∣
∣∣
i.e. →i(3+1)−→j(3−2)+→k(−1−2)=4→i−→j−3→k
Since we need a unit vector in this direction and also making an acute angle with z− axis, the k component must be positive.
Hence we have the answer as −1√26(4→i−→j−3→k)
The vector perpendicular to vectors →a and →b is given by →a×→b.
Similarly, the vector perpendicular to each of the vectors given above is (→i+→j+→k)×(2→i−→j+3→k)=∣∣ ∣ ∣∣→i→j→k1112−13∣∣ ∣ ∣∣
i.e. →i(3+1)−→j(3−2)+→k(−1−2)=4→i−→j−3→k
Since we need a unit vector in this direction and also making an acute angle with z− axis, the k component must be positive.
Hence we have the answer as −1√26(4→i−→j−3→k)
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