## Vectors Quiz-18

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-18
Q1. If the vectors $\stackrel{^}{i}$-3$\stackrel{^}{j}$+2$\stackrel{^}{k}$,-$\stackrel{^}{i}$+2$\stackrel{^}{j}$ represent the diagonals of a parallelogram, them its area will be
•  21
•  √21/2
•  2√21
•  √21/4
Solution

Q2.Let G be the centroid of ∆ABC. If $\stackrel{\to }{a}$B=$\stackrel{\to }{a}$,$\stackrel{\to }{a}$C=$\stackrel{\to }{b}$, then the $\stackrel{\to }{a}$G, in terms of $\stackrel{\to }{a}$ and $\stackrel{\to }{b}$ is
•  2/3($\stackrel{\to }{a}$+$\stackrel{\to }{b}$)
•  1/6($\stackrel{\to }{a}$+$\stackrel{\to }{b}$)
•  1/3($\stackrel{\to }{a}$+$\stackrel{\to }{b}$)
•  1/2($\stackrel{\to }{a}$+$\stackrel{\to }{b}$)
Solution
(a)

Q3.  The unit vector in XOY plane and making angles 45° and 60° respectively with $\stackrel{\to }{a}$=2$\stackrel{^}{i}$+2$\stackrel{^}{j}$-$\stackrel{^}{k}$and b=0$\stackrel{^}{i}$+$\stackrel{^}{j}$-$\stackrel{^}{k}$, is
•   -1/√2 $\stackrel{^}{i}$+1/√2 $\stackrel{^}{k}$
•  1/√2 $\stackrel{^}{i}$-1/√2 $\stackrel{^}{k}$
•  1/(3√2) $\stackrel{^}{i}$+4/(3√2) $\stackrel{^}{j}$+1/(3√2) $\stackrel{^}{k}$
•  None of these
Solution

Q4.
•  2 $\stackrel{\to }{O}$G
•  4 $\stackrel{\to }{O}$G
•  5 $\stackrel{\to }{O}$G
•  3 $\stackrel{\to }{O}$G
Solution
(b)

Q5. The two vectors $\stackrel{\to }{a}$=2$\stackrel{^}{i}$+$\stackrel{^}{j}$+3$\stackrel{^}{k}$,$\stackrel{\to }{b}$=4$\stackrel{^}{i}$$\stackrel{^}{j}$+6$\stackrel{^}{k}$are parallel if λ=
•   2
•  -3
•   3
•  -2
Solution

Q6. Let $\stackrel{\to }{a}$=2$\stackrel{^}{i}$-$\stackrel{^}{j}$+$\stackrel{^}{k}$,$\stackrel{\to }{b}$=$\stackrel{^}{i}$+2$\stackrel{^}{j}$-$\stackrel{^}{k}$and $\stackrel{\to }{c}$=$\stackrel{^}{i}$+$\stackrel{^}{j}$-2$\stackrel{^}{k}$be three vectors. A vector in the plane of $\stackrel{\to }{b}$ and $\stackrel{\to }{c}$ whose projection
on $\stackrel{\to }{a}$ is of magnitude √(2/3) is
•  2$\stackrel{^}{i}$+3$\stackrel{^}{j}$-3$\stackrel{^}{k}$
•  2$\stackrel{^}{i}$+3$\stackrel{^}{j}$+3$\stackrel{^}{k}$
• -2$\stackrel{^}{i}$+5$\stackrel{^}{j}$+5$\stackrel{^}{k}$
•  2$\stackrel{^}{i}$+$\stackrel{^}{j}$+5$\stackrel{^}{k}$
Solution
(a)

Q7. If $\stackrel{\to }{a}$=$\stackrel{^}{i}$+2$\stackrel{^}{j}$+2$\stackrel{^}{k}$and $\stackrel{\to }{b}$=3$\stackrel{^}{i}$+6$\stackrel{^}{j}$+2$\stackrel{^}{k}$, then the vector in the direction of $\stackrel{\to }{a}$ and having magnitude as |$\stackrel{\to }{b}$|, is
•  7($\stackrel{^}{i}$+2$\stackrel{^}{j}$+2$\stackrel{^}{k}$)
•  7/9 ($\stackrel{^}{i}$+2$\stackrel{^}{j}$+2$\stackrel{^}{k}$)
•  7/3 ($\stackrel{^}{i}$+2$\stackrel{^}{j}$+2$\stackrel{^}{k}$)
•  None of these
Solution

Q8. A unit vector $\stackrel{\to }{a}$ makes an angle π/4 with z-axis, if $\stackrel{\to }{a}$+$\stackrel{^}{i}$+$\stackrel{^}{j}$ is a unit vector, then $\stackrel{\to }{a}$ is equal to
•  $\stackrel{^}{i}$/2+$\stackrel{^}{j}$/2+$\stackrel{^}{k}$/2
•  $\stackrel{^}{i}$/2+$\stackrel{^}{j}$/2-$\stackrel{^}{k}$/√2
•  -$\stackrel{^}{i}$/2-$\stackrel{^}{j}$/2+$\stackrel{^}{k}$/√2
•  $\stackrel{^}{i}$/2-$\stackrel{^}{j}$/2-$\stackrel{^}{k}$/√2
Solution

Q9. If the vectors $\stackrel{\to }{a}$=$\stackrel{^}{i}$-$\stackrel{^}{j}$+2$\stackrel{^}{k}$,$\stackrel{\to }{b}$=$\stackrel{^}{i}$+4$\stackrel{^}{j}$+$\stackrel{^}{k}$and $\stackrel{\to }{c}$$\stackrel{^}{i}$+$\stackrel{^}{j}$$\stackrel{^}{k}$ are mutually orthogonal, then (λ,μ) is equal to
•  (-3,2)
•  (2,-3)
•  (-2,3)
•  (3,-2)
Solution

Q10. The vectors 2$\stackrel{^}{i}$+3$\stackrel{^}{j}$-4$\stackrel{^}{k}$and a$\stackrel{^}{i}$+b$\stackrel{^}{j}$+c$\stackrel{^}{k}$are perpendicular when
•  a=2,b=3,c=-4
•  a=4,b=4,c=5
•  a=4,b=4,c=-2
• None of these
Solution

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