COMEDK 2023 Evening Shift | Three Dimensional Geometry Question 5 | Mathematics

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

$$ \left\langle\frac{3}{4}, \quad 0, \quad-\frac{2}{4}\right\rangle $$

$$ \left\langle-\frac{3}{\sqrt{13}}, \quad 0, \quad-\frac{2}{\sqrt{13}}\right\rangle $$

$$ \left\langle 1, \quad 0, \quad-\frac{2}{3}\right\rangle $$

$$ \left\langle\frac{3}{\sqrt{13}}, \quad 0, \quad-\frac{2}{\sqrt{13}}\right\rangle $$

COMEDK 2023 Evening Shift

MCQ (Single Correct Answer)

-0

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

$$-1$$

$$-2$$

COMEDK 2023 Evening Shift

MCQ (Single Correct Answer)

-0

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

$$ \frac{2}{7} \sqrt{35} $$

$$ \frac{1}{7} \sqrt{35} $$

$$ \frac{4}{7} \sqrt{35} $$

$$ \frac{3}{7} \sqrt{35} $$

COMEDK 2023 Evening Shift

MCQ (Single Correct Answer)

-0

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

$$ \vec{b} $$

$$ 2 \vec{a}-\vec{b} $$

$$ \vec{b}-2 \vec{a} $$

$$ \vec{a}-3 \vec{b} $$

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