Algebra and Modulus of Vectors JEE Previous Year Question Bank

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Q 11 :

Let $\vec{A B} = 2 \hat{i} + 4 \hat{j} - 5 \hat{k}$ and $\vec{A D} = \hat{i} + 2 \hat{j} + λ \hat{k}$ , $λ \in ℝ$ . Let the projection of the vector $\vec{v} = \hat{i} + \hat{j} + \hat{k}$ on the diagonal $\vec{A C}$ of the parallelogram ABCD be of length one unit. If $α, β$ , where $α > β$ , be the roots of the equation $λ^{2} x^{2} - 6 λ x + 5 = 0,$ then $2 α - β$ is equal to [2026]

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4
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6

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4

(3)

Q 12 :

Let PQR be a triangle such that $\vec{P Q} = - 2 \hat{i} - \hat{j} + 2 \hat{k}$ and $\vec{P R} = a \hat{i} + b \hat{j} - 4 \hat{k}, a, b \in ℤ$ . Let S be the point on QR which is equidistant from the lines PQ and PR. If $| \vec{P R} | = 9 a n d \vec{P S} = \hat{i} - 7 \hat{j} + 2 \hat{k}$ then the value of $3 a - 4 b$ is: [2026]

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