PYQ Vault
EbooksTutor

Sides or diagonals of a parallelogram built on combinations of two vectors of given length and angle

This type of question, asked 2 times: 13 Apr 2026 S1, 16 Apr 2026 S1. All 2 questions below, oldest first.

Try each one first, then open its answer.

  1. Question 1

    13 Apr 2026 S1

    89
    If a parallelogram is constructed on the vectors aˉ=3pˉ−qˉ,bˉ=pˉ+3qˉ\bar{a} = 3\bar{p} - \bar{q}, \bar{b} = \bar{p} + 3\bar{q} and ∣pˉ∣=3,∣qˉ∣=2|\bar{p}| = 3, |\bar{q}| = 2 and angle between pˉ\bar{p} and qˉ\bar{q} is π3\dfrac{\pi}{3}, then the ratio of the lengths of adjacent sides aˉ\bar{a} and bˉ\bar{b} of the parallelogram is

    Tap an option to check your answer.

  2. Question 2

    16 Apr 2026 S1

    89
    A parallelogram is constructed on 5aˉ+2bˉ5\bar{a} + 2\bar{b} and aˉ−3bˉ\bar{a} - 3\bar{b} as its adjacent sides, with ∣aˉ∣=22,∣bˉ∣=3|\bar{a}| = 2\sqrt{2}, |\bar{b}| = 3 . The angle between aˉ\bar{a} and bˉ\bar{b} is π4\dfrac{\pi}{4} . Then the length of the diagonals of the parallelogram are

    Tap an option to check your answer.