Vectors Quiz-17

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-17
Q1. A vector which makes equal angles with the vectors 1/3 ($\stackrel{^}{i}$-2$\stackrel{^}{j}$+2$\stackrel{^}{k}$), 1/5 (-4$\stackrel{^}{i}$-3$\stackrel{^}{k}$), and $\stackrel{^}{j}$, is
•   5$\stackrel{^}{i}$+$\stackrel{^}{j}$+5$\stackrel{^}{k}$
•  -5$\stackrel{^}{i}$+$\stackrel{^}{j}$+5$\stackrel{^}{k}$
•  -5$\stackrel{^}{i}$+$\stackrel{^}{j}$+5$\stackrel{^}{k}$
•   5$\stackrel{^}{i}$+$\stackrel{^}{j}$-5$\stackrel{^}{k}$
Solution

Q2.If the position vector of A with respect to O is 3$\stackrel{^}{i}$-2$\stackrel{^}{j}$+4$\stackrel{^}{k}$ and $\stackrel{\to }{\mathrm{AB}}$=3$\stackrel{^}{i}$-$\stackrel{^}{j}$+$\stackrel{^}{k}$ Then the position vector of B with respect to O is
•  -$\stackrel{^}{j}$+3$\stackrel{^}{k}$
•  6$\stackrel{^}{i}$-3$\stackrel{^}{j}$+5$\stackrel{^}{k}$
•  $\stackrel{^}{j}$-3$\stackrel{^}{k}$
•  $\stackrel{^}{i}$-3$\stackrel{^}{j}$+5$\stackrel{^}{k}$
Solution

Q3.  If $\stackrel{\to }{a}$=2$\stackrel{^}{i}$-3$\stackrel{^}{j}$+5$\stackrel{^}{k}$, $\stackrel{\to }{b}$=3$\stackrel{^}{i}$-4$\stackrel{^}{j}$+5$\stackrel{^}{k}$ and $\stackrel{\to }{c}$=5$\stackrel{^}{i}$-3$\stackrel{^}{j}$-2$\stackrel{^}{k}$, then the volume of the parallelopiped with
coterminous edges $\stackrel{\to }{a}$+$\stackrel{\to }{b}$,$\stackrel{\to }{b}$+$\stackrel{\to }{c}$,$\stackrel{\to }{c}$+$\stackrel{\to }{a}$ is
•    4
•   5
•  63
•   8
Solution

Q4. Consider a tetrahedron with faces F1,F2,F3,F4. Let $\stackrel{\to }{v}$1, $\stackrel{\to }{v}$2, $\stackrel{\to }{v}$3, $\stackrel{\to }{v}$4be the vectors whose magnitudes are respectively equal to areas of F1,F2,F3,F4 and whose directions are perpendicular to these faces in outward direction. Then, | $\stackrel{\to }{v}$1+ $\stackrel{\to }{v}$2+ $\stackrel{\to }{v}$3+ $\stackrel{\to }{v}$4 | equals
•  1
•  4
•  0
•  None of these
Solution
(c)

Q5. If a tetrahedron has vertices at O(0,0,0),A(1,2,1),B(2,1,3) and C(-1,1,2). Then, the
angle between the faces OAB and ABC will be
•  $$cos^-1(\frac{19}{35})$$
•  $$cos^-1⁡(\frac{17}{31})$$
•  30°
•  90°
Solution
(a)

Q6. If $\stackrel{\to }{a}$,$\stackrel{\to }{b}$,$\stackrel{\to }{c}$ be three non-coplanar vectors and $\stackrel{\to }{p}$,$\stackrel{\to }{q}$,$\stackrel{\to }{r}$ constitute the corresponding reciprocal system of vectors
then for any arbitrary vector$\stackrel{\to }{\alpha }$
•   $\stackrel{\to }{\alpha }$ =( $\stackrel{\to }{\alpha }$$\stackrel{\to }{a}$ ) $\stackrel{\to }{a}$+($\stackrel{\to }{\alpha }$$\stackrel{\to }{b}$ ) $\stackrel{\to }{b}$+( $\stackrel{\to }{\alpha }$$\stackrel{\to }{c}$)$\stackrel{\to }{c}$
•   $\stackrel{\to }{\alpha }$ =( $\stackrel{\to }{\alpha }$$\stackrel{\to }{p}$ ) $\stackrel{\to }{p}$ +( $\stackrel{\to }{\alpha }$$\stackrel{\to }{q}$ ) $\stackrel{\to }{q}$ +( $\stackrel{\to }{\alpha }$$\stackrel{\to }{r}$)r
• $\stackrel{\to }{\alpha }$=($\stackrel{\to }{\alpha }$$\stackrel{\to }{p}$) $\stackrel{\to }{a}$+($\stackrel{\to }{\alpha }$$\stackrel{\to }{q}$) $\stackrel{\to }{b}$+($\stackrel{\to }{\alpha }$$\stackrel{\to }{r}$)$\stackrel{\to }{c}$
•  None of the above
Solution

Q7. A vector of magnitude 12 units perpendicular to the plane containing the vectors 4$\stackrel{^}{i}$+6$\stackrel{^}{j}$-$\stackrel{^}{k}$ and 3$\stackrel{^}{i}$+8$\stackrel{^}{j}$+$\stackrel{^}{k}$is
•  -8$\stackrel{^}{i}$+4$\stackrel{^}{j}$+8$\stackrel{^}{k}$
•  8$\stackrel{^}{i}$+4$\stackrel{^}{j}$+8$\stackrel{^}{k}$
•  8$\stackrel{^}{i}$-4$\stackrel{^}{j}$+8$\stackrel{^}{k}$
•  8$\stackrel{^}{i}$-4$\stackrel{^}{j}$-8$\stackrel{^}{k}$
Solution

Q8. If the scalar projection of the vector x$\stackrel{^}{i}$+$\stackrel{^}{j}$+$\stackrel{^}{k}$ on the vector $\stackrel{^}{i}$-$\stackrel{^}{j}$+5$\stackrel{^}{k}$is 1/√30 then the value of x is
•  -3/2
•  6
•  -6
•  3
Solution

Q9.If $\stackrel{\to }{a}$+$\stackrel{\to }{b}$+$\stackrel{\to }{c}$ are three unit vectors such that $\stackrel{\to }{a}$+$\stackrel{\to }{b}$+$\stackrel{\to }{c}$=0, where $\stackrel{\to }{0}$ is null vector, then $\stackrel{\to }{a}$$\stackrel{\to }{b}$+$\stackrel{\to }{b}$$\stackrel{\to }{c}$+$\stackrel{\to }{c}$$\stackrel{\to }{a}$ is
•  -3
•  -2
•  -3/2
•  0
Solution

Q10. If $\stackrel{\to }{x}$+ $\stackrel{\to }{y}$+ $\stackrel{\to }{z}$= $\stackrel{\to }{0}$,| $\stackrel{\to }{x}$ |=| $\stackrel{\to }{y}$ |+| $\stackrel{\to }{z}$ |=2, and θ is angle between $\stackrel{\to }{y}$ and $\stackrel{\to }{z}$ , then the value of cosec2θ+cot2⁡θ is equal to
•  4/3
•  5/3
•  1/3
• 1
Solution

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Vectors Quiz-17