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Mathematics · 2026 · 2 marks
CBSE 2026 · Region 1 · Set 1 · Q24
Vectors a =3 i -2 j +2 k and b = i +2 k represent the two adjacent sides of a parallelogram. Find the vectors representing its diagonals and hence…
Vectors $\displaystyle \vec{a}=3 \hat{i}-2 \hat{j}+2 \hat{k}$ and $\displaystyle \vec{b}=\hat{i}+2 \hat{k}$ represent the two adjacent sides of a parallelogram. Find the vectors representing its diagonals and hence find their lengths.
Official answer
Diagonals: $\displaystyle \vec{d_1} = 4\hat{i} + 0\hat{j} + 4\hat{k}$ with length $\displaystyle 4\sqrt{2}$; $\displaystyle \vec{d_2} = 2\hat{i} - 2\hat{j}$ with length $\displaystyle 2\sqrt{2}$
Marking-scheme solution
$\displaystyle \vec a + \vec b = 4\hat i - 2\hat j + 4\hat k$, $\displaystyle \vec a - \vec b = 2\hat i - 2\hat j$
The vector representing one of its diagonals is $\displaystyle 4\hat i - 2\hat j + 4\hat k$ or $\displaystyle -(4\hat i - 2\hat j + 4\hat k)$
The vector representing the other diagonal is $\displaystyle 2\hat i - 2\hat j$ or $\displaystyle -(2\hat i - 2\hat j)$
The lengths of the two diagonals are $\displaystyle \sqrt{16+4+16}=6$ and $\displaystyle \sqrt{4+4}=2\sqrt2$
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CBSE Class 12 Mathematics past-paper question from the 2026 board exam, with the answer as CBSE’s own marking scheme gives it. Where our answers come from.