Product of Two Vectors | Vectors jee mains previous year questions

Q 1 :
For three vectors $\vec{A} = (- x \hat{i} - 6 \hat{j} - 2 \hat{k}), \vec{B} = (- \hat{i} + 4 \hat{j} + 3 \hat{k})$ and $\vec{C} = (- 8 \hat{i} - \hat{j} + 3 \hat{k})$ , if $\vec{A} \cdot (\vec{B} \times \vec{C}) = 0$ then value of $x$ is _______ . [2024]

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(4) $\vec{B} = - \hat{i} + 4 \hat{j} + 3 \hat{k} a n d \vec{C} = - 8 \hat{i} - \hat{j} + 3 \hat{k}$

$\vec{B} \times \vec{C} =$ $| \begin{matrix} \hat{i} & \hat{j} & \hat{k} \\ - 1 & 4 & 3 \\ - 8 & - 1 & 3 \end{matrix} |$ $= 15 \hat{i} - 21 \hat{j} + 33 \hat{k}$

$\vec{A} \cdot (\vec{B} \times \vec{C}) = (- x \hat{i} - 6 \hat{j} - 2 \hat{k}) \cdot (15 \hat{i} - 21 \hat{j} + 33 \hat{k})$

$0 = - 15 x + 126 - 66$

$\Rightarrow 15 x = 60 \Rightarrow x = 4$

Q 2 :
Two particles are located at equal distance from origin. The position vectors of those are represented by $\vec{A} = 2 \hat{i} + 3 n \hat{j} + 2 \hat{k}$ and $\vec{B} = 2 \hat{i} - 2 \hat{j} + 4 p \hat{k}$ , respectively. If both the vectors are at right angle to each other, the value of $n^{- 1}$ is __________. [2025]

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(3)

$\vec{A} \cdot \vec{B} = 0 and$ $| \vec{A} |$ $=$ $| \vec{B} |$

$\Rightarrow$ 4 – 6n + 8p = 0

3n – 4p = 2 ... (i)

Also $4 + 9 n^{2} + 4 = 4 + 4 + 16 p^{2}$

$3 n = \pm 4 p$ ... (ii)

$\pm 4 p - 4 p = 2$

Taking –ve sign

–8p = 2

$p = - \frac{1}{4}, 3 n + 1 = 2 \Rightarrow n = \frac{1}{3}$

Topic Question Set

Q 1 :
For three vectors $\vec{A} = (- x \hat{i} - 6 \hat{j} - 2 \hat{k}), \vec{B} = (- \hat{i} + 4 \hat{j} + 3 \hat{k})$ and $\vec{C} = (- 8 \hat{i} - \hat{j} + 3 \hat{k})$ , if $\vec{A} \cdot (\vec{B} \times \vec{C}) = 0$ then value of $x$ is _______ . [2024]

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Topic Question Set

Q 1 : For three vectors A→=(-xi^-6j^-2k^), B→=(-i^+4j^+3k^) and C→=(-8i^-j^+3k^), if A→·(B→×C→)=0 then value of x is _______ . [2024]

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Q 2 : Two particles are located at equal distance from origin. The position vectors of those are represented by A→=2i^+3nj^+2k^ and B→=2i^–2j^+4pk^, respectively. If both the vectors are at right angle to each other, the value of n–1 is __________. [2025]

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Want Us to Email you About Special Offers & Updates?

Q 1 :
For three vectors $\vec{A} = (- x \hat{i} - 6 \hat{j} - 2 \hat{k}), \vec{B} = (- \hat{i} + 4 \hat{j} + 3 \hat{k})$ and $\vec{C} = (- 8 \hat{i} - \hat{j} + 3 \hat{k})$ , if $\vec{A} \cdot (\vec{B} \times \vec{C}) = 0$ then value of $x$ is _______ . [2024]