Let a = 2i + j - 2k, b = i + j and c = a × b. Let d be a vector such that |d - a| = √(11), |c × d| = 3 and the angle between c and d is (π)/4. Then a · d is equal to

Vector Algebra: JEE Main 2026 Mathematics question

JEE Main 2026 · 24 Jan, Morning shift · Q5

JEE Main 202624 Jan, Morning shiftMathematicsMediumVector Algebra184× since 2002

Let

\vec{a} = 2\hat{i} + \hat{j} - 2\hat{k}

\vec{b} = \hat{i} + \hat{j}

and

\vec{c} = \vec{a} \times \vec{b}

. Let

\vec{d}

be a vector such that

|\vec{d} - \vec{a}| = \sqrt{11}

|\vec{c} \times \vec{d}| = 3

and the angle between

\vec{c}

and

\vec{d}

\frac{\pi}{4}

. Then

\vec{a} \cdot \vec{d}

is equal to

JEE Main 2026 · 24 Jan, Morning shift · Q5

JEE Main 202624 Jan, Morning shiftMathematicsMediumVector Algebra184× since 2002

Let

\vec{a} = 2\hat{i} + \hat{j} - 2\hat{k}

\vec{b} = \hat{i} + \hat{j}

and

\vec{c} = \vec{a} \times \vec{b}

. Let

\vec{d}

be a vector such that

|\vec{d} - \vec{a}| = \sqrt{11}

|\vec{c} \times \vec{d}| = 3

and the angle between

\vec{c}

and

\vec{d}

\frac{\pi}{4}

. Then

\vec{a} \cdot \vec{d}

is equal to