Vector Algebra · JEE Main previous year questions

2018 4 questions

1. Q192018 · 16 Apr 2018 · Shift 1

   Let $\vec{a}=\hat{i}+\hat{j}+\hat{k},\vec{c}=\hat{j}-\hat{k}$ and a vector $\vec{b}$ be such that $\vec{a}\times \vec{b}=\vec{c}$ and $\vec{a}\cdot \vec{b}=3$. Then $|\vec{b}|$ equals :

   1. A.$\frac{11}{3}$
   2. B.$\frac{11}{\sqrt{3}}$
   3. C.$\sqrt{\frac{11}{3}}$
   4. D.$\frac{\sqrt{11}}{3}$
   Show answer

   Answer: C

2. Q22018 · 15 Apr 2018 · Shift 1

   If $\lambda \in \mathbf{R}$ is such that the sum of the cubes of the roots of the equation, $x^2+(2-\lambda )x+(10-\lambda )=0$ is minimum, then the magnitude of the difference of the roots of this equation is :

   1. A.$4\sqrt{2}$
   2. B.$2\sqrt{5}$
   3. C.$2\sqrt{7}$
   4. D.20
   Show answer

   Answer: B

3. Q192018 · 15 Apr 2018 · Shift 1

   If $\vec{a},\vec{b}$, and $\vec{c}$ are unit vectors such that $\vec{a}+2\vec{b}+2\vec{c}=\vec{0}$, then $|\vec{a}\times \vec{c}|$ is equal to :

   1. A.$\frac{\sqrt{15}}{4}$
   2. B.$\frac{1}{4}$
   3. C.$\frac{15}{16}$
   4. D.$\frac{\sqrt{15}}{16}$
   Show answer

   Answer: A

4. Q162018 · 8 Apr 2018 · Shift 1

   Let $\vec{u}$ be a vector coplanar with the vectors $\vec{a}=2\hat{i}+3\hat{j}-\hat{k}$ and $\vec{b}=\hat{j}+\hat{k}$. If $\vec{u}$ is perpendicular to $\vec{a}$ and $\vec{u}\cdot \vec{b}=24$, then $|\vec{u}{|}^2$ is equal to

   1. A.$336$
   2. B.$315$
   3. C.$256$
   4. D.$84$
   Show answer

   Answer: A