COMEDK 2023 Evening Shift

The coordinates of the vertices of the triangle are \(A(-2,3,6), B(-4,4,9)\) and \(C(0,5,8)\). The direction cosines of the median \(\mathrm{BE}\) are

\(\mathrm{P} \text { is a point on the line segment joining the points }(3,2,-1) \text { and }(6,2,-2) \text {. If the } x \text { co ordinate of } \mathrm{P} \text { is } 5 \text {, then its } \mathrm{y} \text { coordinate is }\)

The distance of the point \((2,3,4)\) from the line \(1-x=\frac{y}{2}=\frac{1}{3}(1+z)\) is

If the position vector of a point \(A\) is \(\vec{a}+2 \vec{b}\) and \(\vec{a}\) divides \(A B\) in the ratio \(2: 3\), then the position vector of \(B\) is

If the direction ratios of two lines are given by \(3 l m-4 l n+m n=0\) and \(l+2 m+3 n=0\), then the angle between the lines is

\(\text { If } \operatorname{cosec}(90+A)+x \cos A \cot (90+A)=\sin (90+A) \text { then the value of } x \text { is }\)

\(\cos ^6 A-\sin ^6 A \text { is equal to }\)

If \(\cos \alpha=k \cos \beta\) then \(\cot \left(\frac{\alpha+\beta}{2}\right)\) is equal to

The scalar components of a unit vector which is perpendicular to each of the vectors \(\hat{\imath}+2 \hat{\jmath}-\hat{k}\) and \(3 \hat{\imath}-\hat{\jmath}+2 \hat{k}\) are

\(\text { If } \vec{a} \text { and } \vec{b} \text { are unit vectors, then the angle between } \vec{a} \text { and } \vec{b} \text { for which } a-\sqrt{2} \vec{b} \text { is a unit vector is }\)