## Vectors Quiz-16

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-16
Q1. If $\stackrel{\to }{a}$,$\stackrel{\to }{b}$,$\stackrel{\to }{c}$ and $\stackrel{\to }{d}$are the unit vectors such that ($\stackrel{\to }{a}$×$\stackrel{\to }{b}$ )∙($\stackrel{\to }{c}$×$\stackrel{\to }{d}$)=1 and $\stackrel{\to }{a}$$\stackrel{\to }{c}$=1/2,then
•  $\stackrel{\to }{a}$,$\stackrel{\to }{b}$,$\stackrel{\to }{c}$ are non-coplanar
•  $\stackrel{\to }{a}$,$\stackrel{\to }{b}$, $\stackrel{\to }{d}$ are non-coplanar
•  $\stackrel{\to }{b}$, $\stackrel{\to }{d}$ are non-parallel
•  $\stackrel{\to }{a}$, $\stackrel{\to }{d}$ are parallel and $\stackrel{\to }{b}$,$\stackrel{\to }{c}$ are parallel
Solution

Q2.The value of $\stackrel{^}{i}$×($\stackrel{^}{j}$×$\stackrel{^}{k}$)+$\stackrel{^}{j}$×($\stackrel{^}{k}$×$\stackrel{^}{i}$ )+$\stackrel{^}{k}$×($\stackrel{^}{i}$×$\stackrel{^}{j}$) is
•  $\stackrel{\to }{0}$
•  $\stackrel{^}{i}$
•  $\stackrel{^}{j}$
•  $\stackrel{^}{k}$
Solution

Q3.  Let $\stackrel{\to }{a}$ and $\stackrel{\to }{b}$ be two unit vectors such that angle between them is 60°. Then, |$\stackrel{\to }{a}$-$\stackrel{\to }{b}$| is equal to
•  √5
•  √3
•  0
•  1
Solution

Q4. If $\stackrel{\to }{a}$ and $\stackrel{\to }{b}$ are unit vectors such that [$\stackrel{\to }{a}$ $\stackrel{\to }{b}$ $\stackrel{\to }{a}$×$\stackrel{\to }{b}$ ]=1/4, then angle between $\stackrel{\to }{a}$ and $\stackrel{\to }{b}$ is
•  Ï€/3
•  Ï€/4
•  Ï€/6
•  Ï€/2
Solution

Q5. If |$\stackrel{\to }{a}$ |=|$\stackrel{\to }{b}$ |=1 and |$\stackrel{\to }{a}$+$\stackrel{\to }{b}$ |=√3, then the value of (3 $\stackrel{\to }{a}$-4$\stackrel{\to }{b}$ )∙(2$\stackrel{\to }{a}$+5$\stackrel{\to }{b}$ )is
•  -21
•  -21/2
•   21
•  21/2
Solution

Q6. A parallelogram is constructed on 3$\stackrel{\to }{a}$+$\stackrel{\to }{b}$ and $\stackrel{\to }{a}$-4$\stackrel{\to }{b}$, where |$\stackrel{\to }{a}$|=6 and | $\stackrel{\to }{b}$|=8 and $\stackrel{\to }{a}$ and $\stackrel{\to }{b}$
are anti-parallel, then the length of the longer diagonal is
•  40
•  64
• 42
•  48
Solution

Q7. The resultant of ($\stackrel{\to }{p}$-2$\stackrel{\to }{q}$) where. $\stackrel{\to }{p}$=7$\stackrel{^}{i}$-2$\stackrel{^}{j}$+3k ̇ ̂ and $\stackrel{\to }{q}$=3$\stackrel{^}{i}$+$\stackrel{^}{j}$+5k ̇ ̂ is
•  √29
•  4
•  √62-2√35
•  √66
Solution

Q8. If the volume of the tetrahedron whose vertices are (1,-6,10),(-1,-3,7),(5,-1,Î») and (7,-4,7) is 11 cubic units, then Î»=
•  2,6
•  3,4
•  1,7
•  5,6
Solution
(a)

Q9. A non-zero vector $\stackrel{\to }{a}$ is parallel to the line of intersection of the plane determined by vectors $\stackrel{^}{i}$,$\stackrel{^}{i}$-$\stackrel{^}{j}$ and
the plane determined by the vectors $\stackrel{^}{i}$+$\stackrel{^}{j}$, $\stackrel{^}{i}$-$\stackrel{^}{k}$ The angle between $\stackrel{\to }{a}$ and $\stackrel{^}{i}$+2$\stackrel{^}{j}$-2$\stackrel{^}{k}$is
•  Ï€/3
•  Ï€/6
•  Ï€/4
•  None of these
Solution

Q10. The vector $\stackrel{\to }{a}$=Î±$\stackrel{^}{i}$+2$\stackrel{^}{j}$+Î²$\stackrel{^}{k}$lies in the plane of the vectors $\stackrel{\to }{b}$=$\stackrel{^}{i}$+$\stackrel{^}{j}$ and $\stackrel{\to }{c}$=$\stackrel{^}{j}$+$\stackrel{^}{k}$ and bisects the angle between $\stackrel{\to }{b}$ and $\stackrel{\to }{c}$ Then, which one of the following gives possible value of Î± and Î²?
•  Î±=1, Î² =1
•  Î±=2, Î² =2
•  Î±=1,Î²=2
• Î±=2, Î² =1
Solution

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