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Vector Algebra question

2025 · 28 Jan · Shift 1 · Q50

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JEE Main
Mathematics
Vector Algebra
2025 · 28 Jan · Shift 1 · Q50

Vector Algebra question

2025 · 28 Jan · Shift 1 · Q50

JEE MainMathematicsVector AlgebraNumerical+4 / −1

Let

\vec{a}=\hat{\mathrm{i}}+\hat{\mathrm{j}}+\hat{\mathrm{k}}, \overrightarrow{\mathrm{b}}=2 \hat{\mathrm{i}}+2 \hat{\mathrm{j}}+\hat{\mathrm{k}}

and

\overrightarrow{\mathrm{d}}=\vec{a} \times \overrightarrow{\mathrm{b}}

. If

\overrightarrow{\mathrm{c}}

is a vector such that

\vec{a} \cdot \overrightarrow{\mathrm{c}}=|\overrightarrow{\mathrm{c}}|

,

|\overrightarrow{\mathrm{c}}-2 \vec{a}|^2=8

and the angle between

\overrightarrow{\mathrm{d}}

and

\overrightarrow{\mathrm{c}}

is

\frac{\pi}{4}

, then

|10-3 \overrightarrow{\mathrm{~b}} \cdot \overrightarrow{\mathrm{c}}|+|\overrightarrow{\mathrm{d}} \times \overrightarrow{\mathrm{c}}|^2

is equal to

\underline{\hspace{2cm}}

.

Numerical answer

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