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Vector of given length from the angles it makes with the axes

This type of question, asked 3 times: 13 Apr 2026 S1, 15 Apr 2026 S1, 19 May 2026 S1. All 4 questions below, oldest first.

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  1. Question 1

    13 Apr 2026 S1

    90
    A vector rˉ\bar{r} of magnitude 323\sqrt{2} units which makes angles of π4\dfrac{\pi}{4} and π2\dfrac{\pi}{2} respectively with Y and Z axes is

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  2. Question 2

    15 Apr 2026 S1

    96
    If a unit vector makes angles π4\dfrac{\pi}{4} with i^\hat{i}, π3\dfrac{\pi}{3} with j^\hat{j} and θ∈(0,π)\theta \in (0, \pi) with k^\hat{k}, then a value of θ\theta is equal to...

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  3. Question 3

    15 Apr 2026 S1

    90
    The vector rˉ\bar{r} whose magnitude is 323\sqrt{2} units and which makes angles of π4\dfrac{\pi}{4} and π2\dfrac{\pi}{2} with the positive y- and z-axes respectively is....

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  4. Question 4

    19 May 2026 S1

    97
    The position vector of a point PP, such that OPOP inclined to the X axis at 45∘45^\circ and to the Y axis at 60∘60^\circ and ∣OP∣=12|OP| = 12 units is:

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