## Vectrors Quiz-12

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-12
Q1. Two adjacent sides of a parallelogram ABCD are given by $\stackrel{\to }{\mathrm{AB}}$=$\stackrel{^}{i}$+10$\stackrel{^}{j}$+11$\stackrel{^}{k}$ and $\stackrel{\to }{\mathrm{AD}}$=-$\stackrel{^}{i}$+2$\stackrel{^}{j}$+2$\stackrel{^}{k}$
The side AD is rotated by an acute angle α in the plane of the parallelogram so that AD becomes AD'.
If AD' makes a right angle with the side AB, then the cosine of the angle α is given by:
•  8/9
•  √17/9
•  1/9
•  (4√5)/9
Solution

Q2.The volume of the parallelopiped whose coterminous edges are $\stackrel{^}{i}$-$\stackrel{^}{j}$+$\stackrel{^}{k}$, 2$\stackrel{^}{i}$-4$\stackrel{^}{j}$+5$\stackrel{^}{k}$ and 3$\stackrel{^}{i}$-5$\stackrel{^}{j}$+2$\stackrel{^}{k}$, is
•  4 cu unit
•  3 cu unit
•  2 cu unit
•  8 cu unit
Solution
(d)

Q3.  The figure formed by the four points $\stackrel{^}{i}$+$\stackrel{^}{j}$-$\stackrel{^}{k}$ , $\stackrel{^}{i}$+3$\stackrel{^}{j}$ , 5$\stackrel{^}{j}$-2$\stackrel{^}{k}$ and $\stackrel{^}{k}$-$\stackrel{^}{j}$ is
•   Trapezium
•  Rectangle
•  Parallelogram
•  None of these
Solution

Q4. If $\stackrel{\to }{a}$=$\stackrel{^}{i}$-$\stackrel{^}{j}$-$\stackrel{^}{k}$and $\stackrel{\to }{b}$$\stackrel{^}{i}$-3$\stackrel{^}{j}$+$\stackrel{^}{k}$and the orthogonal projection of $\stackrel{\to }{b}$ on $\stackrel{\to }{a}$ is 4/3 ($\stackrel{^}{i}$-$\stackrel{^}{j}$-$\stackrel{^}{k}$)then λ is equal to
•   0
•   2
•  12
•  -1
Solution

Q5. Given vectors $\stackrel{\to }{x}$=3$\stackrel{^}{i}$-6$\stackrel{^}{j}$-$\stackrel{^}{k}$,$\stackrel{\to }{y}$=$\stackrel{^}{i}$+4$\stackrel{^}{j}$-3$\stackrel{^}{k}$ and $\stackrel{\to }{z}$=3$\stackrel{^}{i}$+4$\stackrel{^}{j}$+12$\stackrel{^}{k}$, then the projection of $\stackrel{\to }{x}$×$\stackrel{\to }{y}$ on vector $\stackrel{\to }{z}$ is
•   14
•  -14
•   12
•   15
Solution

Q6. If the position vectors of the vertices of a triangle are 2$\stackrel{^}{i}$-$\stackrel{^}{j}$+$\stackrel{^}{k}$,$\stackrel{^}{i}$-3$\stackrel{^}{j}$-5$\stackrel{^}{k}$and 3$\stackrel{^}{i}$-4$\stackrel{^}{j}$-4$\stackrel{^}{k}$, then the triangle is
•  Equilateral
•  Isosceles
• Right angled isosceles
•  Right angled
Solution
(d)

Q7. If |$\stackrel{\to }{a}$|=|$\stackrel{\to }{b}$|, then ($\stackrel{\to }{a}$+$\stackrel{\to }{b}$)∙($\stackrel{\to }{a}$-$\stackrel{\to }{b}$) is
•  Positive
•  Negative
•  Zero
•  None of these
Solution

Q8.The point collinear with (1,-2,-3)and (2,0,0) among the following is
•  (0,4,6)
•  (0,-4,-5)
•  (0,-4,-6)
•  (0,-4,6)
Solution

Q9. If G is the centroid of ΔABC and G' is the centroid of ΔA'B'C', then A$\stackrel{\to }{\mathrm{A\text{'}}}$+B$\stackrel{\to }{\mathrm{B\text{'}}}$+C$\stackrel{\to }{\mathrm{C\text{'}}}$=
•  2G $\stackrel{\to }{\mathrm{G\text{'}}}$
•  3G $\stackrel{\to }{\mathrm{G\text{'}}}$
•  G $\stackrel{\to }{\mathrm{G\text{'}}}$
•  4G $\stackrel{\to }{\mathrm{G\text{'}}}$
Solution

Q10. The value of [2 $\stackrel{^}{i}$ 3$\stackrel{^}{j}$-5$\stackrel{^}{k}$ ] is equal to
•  -30
•  -25
•   0
• 11
Solution

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