## Vectors Quiz-11

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-11
Q1. If ABCDE is a pentagon, then $\stackrel{\to }{a}$B+$\stackrel{\to }{a}$E+$\stackrel{\to }{b}$C+$\stackrel{\to }{D}$C+$\stackrel{\to }{E}$D+$\stackrel{\to }{a}$C is equal to
•  4 $\stackrel{\to }{a}$C
•  2 $\stackrel{\to }{a}$C
•  3 $\stackrel{\to }{a}$C
•  5 $\stackrel{\to }{a}$C
Solution
Q2.What is the value of ( $\stackrel{\to }{D}$+$\stackrel{\to }{a}$ ]∙[ $\stackrel{\to }{a}$ ×{$\stackrel{\to }{b}$×( $\stackrel{\to }{c}$×$\stackrel{\to }{D}$ )}]?
•  ($\stackrel{\to }{D}$$\stackrel{\to }{a}$ )∙[ $\stackrel{\to }{b}$ $\stackrel{\to }{c}$ $\stackrel{\to }{D}$ ]
•  ($\stackrel{\to }{a}$$\stackrel{\to }{D}$ )∙[ $\stackrel{\to }{b}$ $\stackrel{\to }{c}$ $\stackrel{\to }{D}$ ]
•  ($\stackrel{\to }{b}$$\stackrel{\to }{D}$ )∙[ $\stackrel{\to }{a}$ $\stackrel{\to }{c}$ $\stackrel{\to }{D}$ ]
•  ($\stackrel{\to }{b}$$\stackrel{\to }{D}$ )∙[ $\stackrel{\to }{a}$ $\stackrel{\to }{D}$ $\stackrel{\to }{c}$ ]
Solution

Q3.  If $\stackrel{\to }{a}$,$\stackrel{\to }{b}$,$\stackrel{\to }{c}$ are three non-coplanar vectors and $\stackrel{\to }{p}$,$\stackrel{\to }{q}$,$\stackrel{\to }{r}$, are reciprocal vectors, then (l$\stackrel{\to }{a}$+m$\stackrel{\to }{b}$+n$\stackrel{\to }{c}$)∙(l$\stackrel{\to }{p}$+m$\stackrel{\to }{q}$+n$\stackrel{\to }{r}$) is
•   l+m+n
•  l3+m3+n3
•  l2+m 2+n 2
•  None of these
Solution

Q4. Let ABC be a triangle the position vectors of whose vertices are respectively 7$\stackrel{^}{j}$+10$\stackrel{^}{k}$,-$\stackrel{^}{i}$+6$\stackrel{^}{j}$+6$\stackrel{^}{k}$and -4$\stackrel{^}{i}$+9$\stackrel{^}{j}$+6$\stackrel{^}{k}$. Then, ∆ABC is
•  Isosceles and right angled
•  Equilateral
•  Right angled but not isosceles
•  None of these
Solution

Q5.If $\stackrel{\to }{p}$,$\stackrel{\to }{q}$ and $\stackrel{\to }{r}$ are perpendicular to $\stackrel{\to }{q}$+$\stackrel{\to }{r}$,$\stackrel{\to }{r}$+$\stackrel{\to }{p}$ and $\stackrel{\to }{p}$+$\stackrel{\to }{q}$ respectively and if
|$\stackrel{\to }{p}$+$\stackrel{\to }{q}$ |=6,|$\stackrel{\to }{q}$+$\stackrel{\to }{r}$ |=4√3 and |$\stackrel{\to }{r}$+$\stackrel{\to }{p}$ |=4, then |$\stackrel{\to }{p}$+$\stackrel{\to }{q}$+$\stackrel{\to }{r}$| is
•  5√2
•  10
•  15
•  5
Solution

Q6. If $\stackrel{\to }{a}$=2$\stackrel{^}{i}$+2$\stackrel{^}{j}$+3$\stackrel{^}{k}$,$\stackrel{\to }{b}$=-$\stackrel{^}{i}$+2$\stackrel{^}{j}$+$\stackrel{^}{k}$,$\stackrel{\to }{c}$=3$\stackrel{^}{i}$+$\stackrel{^}{j}$ and $\stackrel{\to }{a}$+t$\stackrel{\to }{b}$ is normal to the vector $\stackrel{\to }{c}$, then the vector of t is
•  8
•  4
• 6
•  2
Solution
(a)

Q7. The value of `a' so that volume of parallelopiped formed by $\stackrel{^}{i}$+a$\stackrel{^}{j}$+$\stackrel{^}{k}$,$\stackrel{^}{j}$+a$\stackrel{^}{k}$and a$\stackrel{^}{i}$+$\stackrel{^}{k}$becomes minimum, is:
•  -3
•   3
•  1/√3
•  √3
Solution

Q8.[$\stackrel{\to }{b}$×$\stackrel{\to }{c}$ $\stackrel{\to }{c}$×$\stackrel{\to }{a}$ $\stackrel{\to }{a}$×$\stackrel{\to }{b}$] is equal to
•  [ $\stackrel{\to }{a}$ $\stackrel{\to }{b}$ $\stackrel{\to }{c}$ ]
•  2[ $\stackrel{\to }{a}$ $\stackrel{\to }{b}$ $\stackrel{\to }{c}$ ]
•  [ $\stackrel{\to }{a}$ $\stackrel{\to }{b}$ $\stackrel{\to }{c}$ ] 2
•  $\stackrel{\to }{a}$ ×($\stackrel{\to }{b}$×$\stackrel{\to }{c}$)
Solution

Q9.
•  -$\stackrel{^}{i}$ +$\stackrel{^}{j}$ -2$\stackrel{^}{k}$
•  2$\stackrel{^}{i}$ -$\stackrel{^}{j}$ +2$\stackrel{^}{k}$
•   $\stackrel{^}{i}$ -$\stackrel{^}{j}$ -2$\stackrel{^}{k}$
•   $\stackrel{^}{i}$ +$\stackrel{^}{j}$ -2$\stackrel{^}{k}$
Solution

Q10. If the vectors $\stackrel{^}{i}$-2x $\stackrel{^}{j}$-3y $\stackrel{^}{k}$and $\stackrel{^}{i}$+3x $\stackrel{^}{j}$+2y $\stackrel{^}{k}$are orthogonal to each other, then the locus of the point (x,y) is
•  A circle
•  An ellipse
•  A parabola
• A straight line
Solution

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