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Vector Algebra question

2024 · 27 Jan · Shift 2 · Q32

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JEE Main
Mathematics
Vector Algebra
2024 · 27 Jan · Shift 2 · Q32

Vector Algebra question

2024 · 27 Jan · Shift 2 · Q32

JEE MainMathematicsVector AlgebraMCQ+4 / −1

Let the position vectors of the vertices

\mathrm{A}, \mathrm{B}

and

\mathrm{C}

of a triangle be

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

and

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

respectively. Let

l_1, l_2

and

l_3

be the lengths of perpendiculars drawn from the ortho center of the triangle on the sides

\mathrm{AB}, \mathrm{BC}

and

\mathrm{CA}

respectively, then

l_1^2+l_2^2+l_3^2

equals:

A
$\frac{1}{4}$
B
$\frac{1}{5}$
C
$\frac{1}{3}$
D
$\frac{1}{2}$

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