## Vectors Quiz-20

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-20
Q1. If ($\stackrel{\to }{a}$×$\stackrel{\to }{b}$ )+($\stackrel{\to }{a}$.$\stackrel{\to }{b}$ ) 2=144 and |$\stackrel{\to }{a}$ |=4, then |$\stackrel{\to }{b}$ |=
•  16
•  8
•  3
•  12
Solution
(c)

Q2.Let, $\stackrel{\to }{a}$=$\stackrel{^}{i}$+2$\stackrel{^}{j}$+$\stackrel{^}{k}$,$\stackrel{\to }{b}$=$\stackrel{^}{i}$-$\stackrel{^}{j}$+$\stackrel{^}{k}$, $\stackrel{\to }{c}$=$\stackrel{^}{i}$+$\stackrel{^}{j}$-$\stackrel{^}{k}$ A vector coplanar to $\stackrel{\to }{a}$ and $\stackrel{\to }{b}$ has a projection along $\stackrel{\to }{c}$ of magnitude 1/√3, then the vector is
•  4$\stackrel{^}{i}$-$\stackrel{^}{j}$+4$\stackrel{^}{k}$
•  4$\stackrel{^}{i}$+$\stackrel{^}{j}$-4$\stackrel{^}{k}$
•  $\stackrel{^}{i}$+$\stackrel{^}{j}$+$\stackrel{^}{k}$
•  None of these
Solution

Q3.  let $\stackrel{\to }{p}$and $\stackrel{\to }{q}$ be the position vectors of P and Q respectively, with respect to O and |$\stackrel{\to }{p}$|=p,|$\stackrel{\to }{q}$|=q.
The points R and S divide PQ internally and externally in the ratio 2 : 3 respectively. If O$\stackrel{\to }{r}$ and $\stackrel{\to }{O}$S are perpendicular, then
•   9p 2=4q 2
•  4p 2=9q 2
•  9p=4q
•  4p=9q
Solution
(a)

Q4. If $\stackrel{\to }{a}$ is perpendicular to $\stackrel{\to }{b}$ and $\stackrel{\to }{r}$ is a non-zero vector such that, p$\stackrel{\to }{r}$+($\stackrel{\to }{r}$.$\stackrel{\to }{b}$ ) $\stackrel{\to }{a}$=$\stackrel{\to }{c}$, then $\stackrel{\to }{r}$=
•  $\stackrel{\to }{c}$/p-(($\stackrel{\to }{b}$.$\stackrel{\to }{c}$ ) $\stackrel{\to }{a}$)/p 2
•  $\stackrel{\to }{a}$/p-(($\stackrel{\to }{c}$.$\stackrel{\to }{a}$ ) $\stackrel{\to }{b}$)/p 2
•  $\stackrel{\to }{b}$/p-(($\stackrel{\to }{a}$.$\stackrel{\to }{b}$ ) $\stackrel{\to }{c}$)/p 2
•  $\stackrel{\to }{c}$/p 2 -(($\stackrel{\to }{b}$.$\stackrel{\to }{c}$ ) $\stackrel{\to }{a}$)/p
Solution
(a)

Q5. Let $\stackrel{\to }{a}$ and $\stackrel{\to }{b}$ be unit vectors inclined at an angle 2α(0≤α≤π) each other, then | $\stackrel{\to }{a}$+$\stackrel{\to }{b}$ |<1, if
•  α=π/2
•  α<π/3
•  α>2π/3
•  π/3 < α < 2π/3
Solution

Q6. Forces of magnitudes 3 and 4 units acting along 6$\stackrel{^}{i}$+2$\stackrel{^}{j}$+3$\stackrel{^}{k}$and 3$\stackrel{^}{i}$-2$\stackrel{^}{j}$+6$\stackrel{^}{k}$respectively act on a particle and
displace it from (2,2-1) to (4,3,1). The work done is
•  120/7
• 125/7
•  121/7
Solution

Q7. If the position vectors of three points A,B,C are respectively $\stackrel{^}{i}$+$\stackrel{^}{j}$+$\stackrel{^}{k}$,2$\stackrel{^}{i}$+3$\stackrel{^}{j}$-4$\stackrel{^}{k}$and 7$\stackrel{^}{i}$+4$\stackrel{^}{j}$+9$\stackrel{^}{k}$,
then the unit vector perpendicular to the plane of triangle ABC is
•  31$\stackrel{^}{i}$-18$\stackrel{^}{j}$-9$\stackrel{^}{k}$
•  (31$\stackrel{^}{i}$-38$\stackrel{^}{j}$-9$\stackrel{^}{k}$)/√2486
•  (31$\stackrel{^}{i}$+38$\stackrel{^}{j}$+9$\stackrel{^}{k}$)/√2486
•  None of these
Solution

Q8.If $\stackrel{\to }{a}$+$\stackrel{\to }{b}$+$\stackrel{\to }{c}$=$\stackrel{\to }{0}$ and |$\stackrel{\to }{a}$ |=3,|$\stackrel{\to }{b}$ |=5,$\stackrel{\to }{a}$+|$\stackrel{\to }{c}$ |=7, then angle between $\stackrel{\to }{a}$ and $\stackrel{\to }{b}$ is
•  π/6
•  π/3
•  π/2
•  π
Solution

Q9.
•  ∆=0
•  ∆=1
•  ∆= any non-zero value
•  None of these
Solution

Q10. A unit vector in xy-plane that makes an angle 45° with the vector
($\stackrel{^}{i}$+$\stackrel{^}{j}$) and an angle of 60° with the vector (3$\stackrel{^}{i}$-4$\stackrel{^}{j}$), is

•  $\stackrel{^}{i}$
•  1/√2($\stackrel{^}{i}$-$\stackrel{^}{j}$)
•  1/√2($\stackrel{^}{i}$+$\stackrel{^}{j}$)
• None of these
Solution

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