Vector Algebra · JEE Main previous year questions

2022 27 questions

1. Q262022 · 25 Jun 2022 · Shift 2· Numerical answer

   Let $\vec{b}=\hat{i}+\hat{j}+\lambda \hat{k}$, $\lambda \in \mathbb{R}$. If $\vec{a}$ is a vector such that $\vec{a}\times \vec{b}=13\hat{i}-\hat{j}-4\hat{k}$ and $\vec{a}\cdot \vec{b}+21=0$, then $(\vec{b}-\vec{a})\cdot (\hat{k}-\hat{j})+(\vec{b}+\vec{a})\cdot (\hat{i}-\hat{k})$ is equal to $\underline{}$.

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   Answer: 14

2. Q132022 · 24 Jun 2022 · Shift 2

   Let $\hat{a}$ and $\hat{b}$ be two unit vectors such that $|(\hat{a}+\hat{b})+2(\hat{a}\times \hat{b})|=2$. If $\theta \in (0,\pi )$ is the angle between $\hat{a}$ and $\hat{b}$, then among the statements : (S1) : $2|\hat{a}\times \hat{b}|=|\hat{a}-\hat{b}|$ (S2) : The projection of $\hat{a}$ on $(\hat{a}+\hat{b})$ is $\frac{1}{2}$

   1. A.Only (S1) is true.
   2. B.Only (S2) is true.
   3. C.Both (S1) and (S2) are true.
   4. D.Both (S1) and (S2) are false.
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   Answer: C