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11 months ago

Class 12th Maths

Let $\vec{a} = \hat{i} - \hat{j} + 2 \hat{k} a n d l e t \hat{b}$ be a vector such that $\vec{a} * \vec{b} = 2 \hat{i} - \hat{k} a n d \vec{a}, \vec{b} = 3 .$ Then the projection of $\vec{b}$ on the vector $\vec{a} - \vec{b} i s :$

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Payal Gupta

Contributor-Level 10

$\vec{a} = \hat{i} - \hat{j} + 2 \hat{k}$

$\vec{a} * \vec{b} = 2 \hat{i} - \hat{k}$

$\vec{a} . \vec{b} = 3$

${| \vec{a} * \vec{b} |}^{2} + {| \vec{a} . \vec{b} |}^{2} = {| \vec{a} |}^{2} . {| \vec{b} |}^{2}$

$= \frac{\vec{b} . \vec{a} - {| \vec{b} |}^{2}}{| \vec{a} - \vec{b} |} = \frac{3 - \frac{7}{3}}{\sqrt[]{\frac{7}{3}}} = \frac{2}{\sqrt[]{21}}$

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11 months ago

Class 12th Physics

In the circuit, the logical value of A = 1 or B = 1 when potential at A or B is 5 V and the logical value of A = 0 or B = 0 when potential at A or B is 0 V. The truth table of the given circuit will be:

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Vishal Baghel

Contributor-Level 10

When both A and B have logical value 'l' both diode are reverse bias and current will flow in resistor hence output will be 5 volt i.e. logical value '1'.

In all other case conduction will take place hence output will be zero value i.e. logical value 'o'.

So truth table is

A B Y

0 0

0 1 0 (AND gate)

...more

0 0

New answer posted

11 months ago

Class 12th Maths

The shortest distance between the lines $\frac{x + 7}{- 6} = \frac{y - 6}{7} = Z a n d \frac{7 - x}{2} = y - 2 = z - 6$ is

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Payal Gupta

Contributor-Level 10

$A (- 7 \hat{i} + 6 \hat{j}) C (7 \hat{i} + 2 \hat{j} + 6 \hat{k})$

$\vec{b} = - 6 \hat{i} + 7 \hat{j} + \hat{k}$ $\vec{d} = - 2 \hat{i} + \hat{j} + \hat{k}$

$\vec{b} * \vec{d} = | \begin{matrix} \hat{i} & \hat{j} & \hat{k} \\ - 6 & 7 & 1 \\ - 2 & 1 & 1 \end{matrix} | = 3 \hat{i} + 2 \hat{j} + 4 \hat{k}$

the shortest distance between the lines

$=$ $| \frac{42 - 8 + 24}{29} |$ $=$ $\frac{58}{29}$ $=$ $2$

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New answer posted

11 months ago

Class 12th Physics

The magnetic moment of an electron (e) revolving in an orbit around nucleus with an orbital angular momentum is given by:

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Vishal Baghel

Contributor-Level 10

Kindly consider the following answer

$\vec{μ} = - \frac{e}{2 m} \vec{L}$

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11 months ago

Class 12th Atoms

The momentum of an electron revolving in nth orbit is given by:

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Vishal Baghel

Contributor-Level 10

mvr = $\frac{n h}{2 π}$ $\frac{}{}$

So momentum (mv) = $\frac{n h}{2 π r}$

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11 months ago

Class 12th Maths

A plane E is perpendicular to the two planes 2x – 2y + z = 0 and x – y + 2z = 4, and passes through the point P(1, -1, 1). If the distance of the plane E from the point Q(a, a, 2) is $3 \sqrt[]{2},$ then (PQ)² is equal to

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Payal Gupta

Contributor-Level 10

First plane, P₁ = 2x – 2y + z = 0,

normal vector $\equiv n_{1} = (2, - 2, 1)$

Second plane, P₂ = x – y + 2z = 4,

normal vector $\equiv n_{2} = (1, - 1, 2)$

Plane perpendicular to P₁ and P₂ will have normal vector n₃ where n₃ = (n₁* n₂)

Hence,

n₃ = (3, 0)

Distance PQ

$= \sqrt[]{21} \Rightarrow {(P Q)}^{2} = 21$

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11 months ago

Class 12th Physics

A metal exposed to light of wavelength 800nm and emits photoelectrons with a certain kinetic energy. The maximum kinetic energy of photo-electron doubles when light of wavelength 500nm is used. The work function of the metal is: (Take hc = 1230 eV –nm).

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Vishal Baghel

Contributor-Level 10

$_{} \frac{}{}$ $K . E_{1} = \frac{1230}{800} - ?$ - (i)

$_{}_{} \frac{}{}$ $K . E_{2} = 2 K . E_{1} = \frac{1230}{500} - ?$ - (ii)

from (i) & (ii)

$? = 0.615$ ev

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11 months ago

Class 12th Physics

A thin lens made of glass (refractive index $= 1.5$ ) of focal length $f = 16 c m$ is immersed in a liquid of refractive index 1.42. If its focal length in liquid is $f_{l}$ , then the ratio $f_{l}$ /f is closest to the integer:

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alok kumar singh

Contributor-Level 10

$\frac{1}{f} = (μ_{g} - 1) (\frac{1}{R_{1}} - \frac{1}{R_{2}})$

$\frac{1}{f_{l}} = (\frac{μ_{g}}{μ_{l}} - 1) (\frac{1}{R_{1}} - \frac{1}{R_{2}})$

(i) $\frac{f_{l}}{f} = \frac{μ_{g} - 1}{\frac{μ_{g}}{μ_{l}} - 1} = \frac{1.5 - 1}{\frac{1.5}{1.41} - 1} = 8.875 \approx 9$

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11 months ago

Class 12th Physics

Time taken by light to travel in two different materials A and B refractive indices $μ_{A} a n d μ_{B}$ of same thickness is $t_{1} a n d t_{2}$ respectively. It $t_{2} - t_{1} = 5 * 1 0^{- 10} s$ and the ratio of $μ_{A} t o μ_{B}$ 1 : 2. Then, the thickness of material, in meter is: (Given $υ_{A} a n d υ_{B}$ are velocities of light in A and B materials respectively.)

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Vishal Baghel

Contributor-Level 10

$\frac{μ_{A}}{μ_{B}} = \frac{C / v_{A}}{C / v_{B}} = \frac{v_{B}}{v_{A}} = \frac{1}{2}$

Let the thickness is d

$d = \frac{5 * 1 0^{- 10} * v_{A} v_{B}}{v_{A} - v_{B}}$

d = 5 * 10^-10 * v_A

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New answer posted

11 months ago

Class 12th Chemistry

Which of the following methods are not used to refine any metal?

(A). Liquation

(B). Calcination

(C). Electrolysis

(D). Leaching

(E). Distillation

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alok kumar singh

Contributor-Level 10

Calcination and leaching are the methods of concentration of ores and not that of refining.

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