Vectors Quiz-19

Vectors Quiz-19

Dear Readers,

As per analysis for previous years, it has been observed that students preparing for JEE MAINS find Mathematics out of all the sections to be complex to handle and the majority of them are not able to comprehend the reason behind it. This problem arises especially because these aspirants appearing for the examination are more inclined to have a keen interest in Mathematics due to their ENGINEERING background. Furthermore, sections such as Mathematics are dominantly based on theories, laws, numerical in comparison to a section of Engineering which is more of fact-based, Physics, and includes substantial explanations. By using the table given below, you easily and directly access to the topics and respective links of MCQs. Moreover, to make learning smooth and efficient, all the questions come with their supportive solutions to make utilization of time even more productive. Students will be covered for all their studies as the topics are available from basics to even the most advanced..

Q1. If the vectors $\overrightarrow{\mathrm{r1}}$=a$\hat{i}$+$\hat{j}$+$\hat{k}$, $\overrightarrow{\mathrm{r2}}$=$\hat{i}$+b$\hat{j}$+$\hat{k}$, $\overrightarrow{\mathrm{r3}}$=$\hat{i}$+$\hat{j}$+c$\hat{k}$ (a≠1,b≠1,c≠1) are coplanar,
then the value of 1/(1-a)+1/(1-b)+1/(1-c), is

•  -1
•  0
•  1
•  None of these

Solution

Q2.If $\overrightarrow{a}$,$\overrightarrow{b}$,$\overrightarrow{c}$ are non-coplanar vectors and λ be a real number, then the vectors $\overrightarrow{a}$+2$\overrightarrow{b}$+3$\overrightarrow{c}$,λ $\overrightarrow{b}$+4 $\overrightarrow{c}$ and (2λ-1) $\overrightarrow{c}$ are non-coplanar for

•  All values of λ
•  All except one value of λ
•  All except two values of λ
•  No value of λ

Solution

Q3.  The value of a so that the volume of parallelopiped formed by $\hat{i}$+a$\hat{j}$+$\hat{k}$, $\hat{j}$+a$\hat{k}$ and a$\hat{i}$+$\hat{k}$ becomes minimum is

•   -3
•   3
•  1/√3
•  √3

Solution

Q4. The area of parallelogram constructed on the vectors $\overrightarrow{a}$= $\overrightarrow{p}$ +2 $\overrightarrow{q}$ and $\overrightarrow{b}$=2 $\overrightarrow{p}$ + $\overrightarrow{q}$ , where $\overrightarrow{p}$ and $\overrightarrow{q}$ are unit vectors forming an angle of 30° is

•  3/2
•  5/2
•  7/2
•  None of these

Solution
(a)

Q5. If |$\overrightarrow{a}$ |=3,|$\overrightarrow{b}$ |=4, then a value of λ for which $\overrightarrow{a}$+λ$\overrightarrow{b}$ is perpendicular to $\overrightarrow{a}$-λ$\overrightarrow{b}$ is

•  9/16
•  3/4
•  3/2
•  4/3

Solution
 

Q6. Given, $\overrightarrow{p}$=3$\hat{i}$+2$\hat{j}$+4$\hat{k}$, $\overrightarrow{a}$=$\hat{i}$+$\hat{j}$, $\overrightarrow{b}$=$\hat{j}$+$\hat{k}$, $\overrightarrow{c}$=$\hat{i}$+$\hat{k}$and $\overrightarrow{p}$=x$\overrightarrow{a}$+ y$\overrightarrow{b}$+z$\overrightarrow{b}$ , then x,y,z are respectively

•  3/2 ,1/2 ,5/2
•  1/2 ,3/2 ,5/2
• 5/2 ,3/2 ,1/2
•  1/2 ,5/2 ,3/2

Solution

Q7. If $\overrightarrow{a}$,$\overrightarrow{b}$,$\overrightarrow{c}$ are three vectors such that $\overrightarrow{a}$=$\overrightarrow{b}$+$\overrightarrow{c}$ and the angle between $\overrightarrow{b}$ and $\overrightarrow{c}$ is π/2, then

•  a ²=b ²+c ²
•  b ²=c ²+a ²
•  c ²=a ²+b ²
•  2a ²-b ²=c ²

Solution
(a)

Q8. The values of x for which the angle between the vectors $\overrightarrow{a}$=x$\hat{i}$-3$\hat{j}$-$\hat{k}$and $\overrightarrow{b}$=2x$\hat{i}$+x$\hat{j}$-$\hat{k}$is acute
and the angle between the vector $\overrightarrow{b}$ and the y-axis lies between π/2 and π are

•  1, 2
•  -2,-3
•  All x< 0
•  All x>0

Solution

Q9. If $\overrightarrow{p}$=$\hat{i}$+$\hat{j}$, $\overrightarrow{q}$=4$\hat{k}$-$\hat{j}$ and $\overrightarrow{r}$=$\hat{i}$+$\hat{k}$,then the unit vector in the direction of 3$\overrightarrow{p}$+$\overrightarrow{q}$-2$\overrightarrow{r}$ is

•  1/3 ($\hat{i}$+2$\hat{j}$+2$\hat{k}$)
•  1/3 ($\hat{i}$-2$\hat{j}$-2$\hat{k}$)
•  1/3 ($\hat{i}$-2$\hat{j}$+2$\hat{k}$)
•  $\hat{i}$+2$\hat{j}$+2$\hat{k}$

Solution

Q10. If ABCDEF is a regular hexagon with $\overrightarrow{a}$B=$\overrightarrow{a}$ and $\overrightarrow{b}$C=$\overrightarrow{b}$, then $\overrightarrow{c}$E equals

•  $\overrightarrow{b}$-$\overrightarrow{a}$
•  -$\overrightarrow{b}$
•  $\overrightarrow{b}$-2$\overrightarrow{a}$
• $\overrightarrow{b}$+$\overrightarrow{a}$

Solution