## Vectors Quiz-15

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..
Vectors Quiz-15
Q1. If $\stackrel{\to }{a}$×($\stackrel{\to }{b}$×$\stackrel{\to }{c}$ )=($\stackrel{\to }{a}$×$\stackrel{\to }{b}$$\stackrel{\to }{c}$, where $\stackrel{\to }{a}$, $\stackrel{\to }{b}$ and $\stackrel{\to }{c}$ are any three vectors such that $\stackrel{\to }{a}$.$\stackrel{\to }{b}$≠0, $\stackrel{\to }{b}$$\stackrel{\to }{c}$≠0, then $\stackrel{\to }{a}$ and $\stackrel{\to }{c}$ are
•  inclined at angle of π/6 between them
•  Perpendicular
•  Parallel
•  inclined at an angle of π/3 between them
Solution

Q2.Let $\stackrel{\to }{a}$, $\stackrel{\to }{b}$,$\stackrel{\to }{c}$ are three non-coplanar vectors such that $\stackrel{\to }{\mathrm{r1}}$=$\stackrel{\to }{a}$-$\stackrel{\to }{b}$+$\stackrel{\to }{c}$, $\stackrel{\to }{\mathrm{r2}}$=$\stackrel{\to }{b}$+$\stackrel{\to }{c}$-$\stackrel{\to }{a}$, $\stackrel{\to }{\mathrm{r3}}$=$\stackrel{\to }{c}$+$\stackrel{\to }{a}$+$\stackrel{\to }{b}$,$\stackrel{\to }{r}$=2$\stackrel{\to }{a}$-3$\stackrel{\to }{b}$+4$\stackrel{\to }{c}$
•  λ1=7
•  λ13=3
•  λ123=3
•  λ32=2
Solution

Q3.  If the vectors $\stackrel{\to }{c}$,$\stackrel{\to }{a}$=x$\stackrel{^}{i}$+y$\stackrel{^}{j}$+z$\stackrel{^}{k}$and $\stackrel{\to }{b}$=$\stackrel{^}{j}$ are such that $\stackrel{\to }{a}$,$\stackrel{\to }{c}$ and $\stackrel{\to }{b}$ from a right handed system, then $\stackrel{\to }{c}$ is
•   z$\stackrel{^}{i}$-x$\stackrel{^}{k}$
•   $\stackrel{\to }{0}$
•  y$\stackrel{^}{j}$
•  -z$\stackrel{^}{i}$-x$\stackrel{^}{k}$
Solution

Q4. The medium AD of the triangle ABC is bisected at E,BE meets AC in F, then AF:AC=
•  3/4
•  1/3
•  1/2
•  1/4
Solution

Q5.If the points with position vectors 60$\stackrel{^}{i}$+3$\stackrel{^}{j}$,40$\stackrel{^}{i}$-8$\stackrel{^}{j}$ and a$\stackrel{^}{i}$-52$\stackrel{^}{j}$ are collinear, then a is equal to
•  -40
•  -20
•   20
•   40
Solution

Q6.
•  All the three vectors are parallel to one and the same plane
•  All the three vectors are linearly dependent
• This system of equation has a non-trivial solution
•  All the three vectors are perpendicular to each other
Solution
(a)

Q7. The length of the shortest distance between the two lines $\stackrel{\to }{r}$=(-3$\stackrel{^}{i}$+6$\stackrel{^}{j}$)+s(-4$\stackrel{^}{i}$+3$\stackrel{^}{j}$+2$\stackrel{^}{k}$) and $\stackrel{\to }{r}$=(-$\stackrel{^}{i}$+7$\stackrel{^}{k}$)+t(-4$\stackrel{^}{i}$+$\stackrel{^}{j}$+$\stackrel{^}{k}$) is
•   7 units
•  13 units
•   8 units
•   9 units
Solution

Q8.Let $\stackrel{^}{u}$ and $\stackrel{^}{v}$ are unit vectors such that $\stackrel{^}{u}$$\stackrel{^}{v}$=0 If r ̂ is any vector coplanar with $\stackrel{^}{u}$ and $\stackrel{^}{v}$, then the magnitude of the vector $\stackrel{\to }{r}$×($\stackrel{^}{u}$×$\stackrel{^}{v}$ ) is
•  0
•  1
•  |$\stackrel{\to }{r}$|
•  2|$\stackrel{\to }{r}$|
Solution

Q9. A force of magnitude √6 acting along the line joining the points A(2,-1,1) and B(3,1,2) displaces a particle from A to B. The work done by the force is
•  6
•  6√6
•  √6
•  12
Solution

Q10. If $\stackrel{\to }{a}$$\stackrel{\to }{b}$$\stackrel{\to }{c}$ and $\stackrel{\to }{p}$ , $\stackrel{\to }{q}$ ,$\stackrel{\to }{r}$ are reciprocal system of vectors, then $\stackrel{\to }{a}$× $\stackrel{\to }{p}$ +$\stackrel{\to }{b}$× $\stackrel{\to }{q}$ +$\stackrel{\to }{c}$×$\stackrel{\to }{r}$ equals
•  [$\stackrel{\to }{a}$$\stackrel{\to }{b}$$\stackrel{\to }{c}$ ]
•  ( $\stackrel{\to }{p}$ + $\stackrel{\to }{q}$ +$\stackrel{\to }{r}$ )
•   $\stackrel{\to }{0}$
• $\stackrel{\to }{a}$+$\stackrel{\to }{b}$+$\stackrel{\to }{c}$
Solution

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