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Vector Algebra question

2025 · 23 Jan · Shift 1 · Q30

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JEE Main
Mathematics
Vector Algebra
2025 · 23 Jan · Shift 1 · Q30

Vector Algebra question

2025 · 23 Jan · Shift 1 · Q30

JEE MainMathematicsVector AlgebraMCQ+4 / −1

Let the position vectors of the vertices

\mathrm{A}, \mathrm{B}

and C of a tetrahedron ABCD be

\hat{\mathbf{i}}+2 \hat{\mathbf{j}}+\hat{\mathrm{k}}, \hat{\mathrm{i}}+3 \hat{\mathrm{j}}-2 \hat{k}

and

2 \hat{i}+\hat{j}-\hat{k}

respectively. The altitude from the vertex

D

to the opposite face

A B C

meets the median line segment through

A

of the triangle

A B C

at the point

E

. If the length of

A D

is

\frac{\sqrt{110}}{3}

and the volume of the tetrahedron is

\frac{\sqrt{805}}{6 \sqrt{2}}

, then the position vector of E is

A
$\frac{1}{6}(7 \hat{\mathrm{i}}+12 \hat{\mathrm{j}}+\hat{\mathrm{k}})$
B
$\frac{1}{12}(7 \hat{\mathrm{i}}+4 \hat{\mathrm{j}}+3 \hat{\mathrm{k}})$
C
$\frac{1}{6}(12 \hat{i}+12 \hat{j}+\hat{k})$
D
$\frac{1}{2}(\hat{i}+4 \hat{j}+7 \hat{k})$

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