In a triangle ABC , right angled at the vertex A , if the position vectors of A , B and C are respectively `3 hati + hatj-hatk , -hati + 3hatj + phatk` and `5 hati + q hatj - 4 hatk` , then the point (p,q) lies on a lineA. parallel to y-axisB. making an acute angle with the positive direction of x-axisC. parallel to x-axisD. making an obtuse angle with the positive direction of x axis

In a triangle ABC , right angled at the vertex A , if the position vec

1.	In a triangle ABC , right angled at the vertex A , if the position vectors of A , B and C are respectively `3 hati + hatj-hatk , -hati + 3hatj + phatk` and `5 hati + q hatj - 4 hatk` , then the point (p,q) lies on a lineA. parallel to y-axisB. making an acute angle with the positive direction of x-axisC. parallel to x-axisD. making an obtuse angle with the positive direction of x axis
Answer» Correct Answer - B We find that `vecAB = - 4hati + 2 hatj + (p+1) hatk` and `vecAC = 2 hati + (q -1) hatj - 3hatk` . It is given that the triangle is right angled at A . `therefore vec(AB) * vec(AC) = 0 implies -8 + 2q -2- 3p - 3 = 0 implies 3p-2p + 13 = 0` Hence , (p,q) lies on the line 3x - 2y + 13 = 0 . This line makes an acute angle with the positive direction of x - axis .

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