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Recent questions tagged sec3

Show that each of the given three vectors is a unit vector: $ \large\frac{1}{7}$$ ( 2\hat i + 3\hat j + 6\hat k),\large\frac{1}{7}$$ ( 3\hat i - 6\hat j + 2\hat k), \large\frac{1}{7}$$ ( 6\hat i + 2\hat j - 3\hat k) $ Also, show that they are mutually perpendicular to each other.

asked Dec 6, 2012 by thanvigandhi_1

1 answer

Find $| \overrightarrow a |$ and $| \overrightarrow b |$ , if $(\overrightarrow a + \overrightarrow b) ⋅ (\overrightarrow a − \overrightarrow b) = 8$ and $| \overrightarrow a |= 8 | \overrightarrow b |.$

asked Dec 6, 2012 by thanvigandhi_1

1 answer

Evaluate the product $(3\overrightarrow a − 5\overrightarrow b) ⋅ (2\overrightarrow a + 7\overrightarrow b)$

asked Dec 6, 2012 by thanvigandhi_1

1 answer

Find the magnitude of two vectors $ \overrightarrow a$ and $\overrightarrow b$ , having the same magnitude and such that the angle between them is $60^{\omicron}$ and their scalar product is $\large \frac{1}{2}$.

asked Dec 6, 2012 by thanvigandhi_1

1 answer

Find $| \overrightarrow x |$, if for a unit vector $\overrightarrow a , (\overrightarrow x − \overrightarrow a) ⋅ (\overrightarrow x + \overrightarrow a) =12$.

asked Dec 6, 2012 by thanvigandhi_1

1 answer

If $\overrightarrow a = 2\hat i + 2\hat j + 3\hat k,\: \overrightarrow b = − \hat i + 2\hat j + \hat k$ and $ \overrightarrow c = 3\hat i + \hat j$ are such that $\overrightarrow a + λ\overrightarrow b $ is perpendicular to $ \overrightarrow c $ , then find the value of $λ.$

asked Dec 6, 2012 by thanvigandhi_1

1 answer

Show that $| \overrightarrow a | \overrightarrow b + | \overrightarrow b | \overrightarrow a$ is perpendicular to $| \overrightarrow a | \overrightarrow b - | \overrightarrow b | \overrightarrow a$, for any two nonzero vectors $\overrightarrow a$ and $\overrightarrow b$.

asked Dec 6, 2012 by thanvigandhi_1

1 answer

If $ \overrightarrow a . \overrightarrow a = 0$ and $ \overrightarrow a . \overrightarrow b = 0$, then what can be concluded about the vector $\overrightarrow b$?

asked Dec 6, 2012 by thanvigandhi_1

1 answer

If $ \overrightarrow a, \overrightarrow b, \overrightarrow c, $are unit vectors such that $ \overrightarrow a + \overrightarrow b + \overrightarrow c = \overrightarrow 0$, find the value of $ \overrightarrow a ⋅ \overrightarrow b + \overrightarrow b ⋅ \overrightarrow c + \overrightarrow c ⋅ \overrightarrow a$.

asked Dec 6, 2012 by thanvigandhi_1

1 answer

If either vector \(\overrightarrow a = \overrightarrow 0\) or \(\overrightarrow b = \overrightarrow 0\), then \(\overrightarrow a . \overrightarrow b = 0\). But the converse need not be true. Justify your answer with an example.

asked Dec 6, 2012 by thanvigandhi_1

1 answer

If the vertices $A, B, C$ of a triangle $ABC$ are $(1, 2, 3), (-1, 0, 0), (0, 1, 2)$ respectively, then find $ \angle ABC. \angle ABC$ is the angle between the vectors $ \overline {BA}$ and $\overline {BC}$.

asked Dec 6, 2012 by thanvigandhi_1

1 answer

Show that the points A(1, 2, 7), B(2, 6, 3) and C(3, 10, –1) are collinear.

asked Dec 6, 2012 by thanvigandhi_1

1 answer

Show that the vectors \(2\hat i - \hat j + \hat k, \: \hat i - 3\hat j - 5\hat k\) and \(3\hat i - 4\hat j - 4\hat k\) form the vertices of a right angled triangle.

asked Dec 6, 2012 by thanvigandhi_1

1 answer

If $\overrightarrow a$ is a nonzero vector of magnitude $" a "$ and $λ$ a nonzero scalar, then $λ \overrightarrow a$ is unit vector if

asked Dec 6, 2012 by thanvigandhi_1

1 answer

Find the integrals of the functions\[\sin^2(2x+5)\]

asked Dec 5, 2012 by sreemathi.v

1 answer

Find the integral of the function: $\int sin(3x). cos(4x) dx$

asked Dec 5, 2012 by sreemathi.v

1 answer

Find the integrals of the functions\[\cos2x\;\cos4x\;\cos6x\]

asked Dec 5, 2012 by sreemathi.v

1 answer

Find the integrals of the functions\[\sin^3(2x+1)\]

asked Dec 5, 2012 by sreemathi.v

1 answer

Find the integrals of the functions\[\sin^3x\;\cos^3x\]

asked Dec 5, 2012 by sreemathi.v

1 answer

Find the integrals of the functions $\sin x\;\sin2x\;\sin3x$

asked Dec 5, 2012 by sreemathi.v

1 answer

Find the integrals of the functions\[\sin4x\;\sin8x\]

asked Dec 5, 2012 by sreemathi.v

1 answer

Find the integrals of the functions $\frac{1-\cos x}{1+\cos x}$

asked Dec 5, 2012 by sreemathi.v

1 answer

Find the integrals of the functions $\frac{\cos x}{1+\cos x}$

asked Dec 5, 2012 by sreemathi.v

1 answer

Find the integrals of the functions\[\sin^4x\]

asked Dec 5, 2012 by sreemathi.v

1 answer

Find the integrals of the functions\[\cos^42x\]

asked Dec 5, 2012 by sreemathi.v

1 answer

Find the integrals of the functions $\frac{\sin^2x}{1+\cos x}$

asked Dec 5, 2012 by sreemathi.v

1 answer

Find the integrals of the functions\[\frac{\cos2x-\cos2\alpha}{\cos x-\cos\alpha}\]

asked Dec 5, 2012 by sreemathi.v

1 answer

Find the integrals of the functions\[\frac{\cos x-\sin x}{1+\sin2x}\]

asked Dec 5, 2012 by sreemathi.v

1 answer

Find the integrals of the functions\[\tan^32x\sec2x\]

asked Dec 5, 2012 by sreemathi.v

1 answer

Find the integrals of the functions $\tan^4x$

asked Dec 5, 2012 by sreemathi.v

1 answer

Find the integrals of the functions $\frac{\sin^3x+\cos^3x}{\sin^2x\cos^2x}$

asked Dec 5, 2012 by sreemathi.v

1 answer

Find the integrals of the functions $\frac{\cos2x+2\sin^2x}{\cos^2x}$

asked Dec 5, 2012 by sreemathi.v

1 answer

Find the integrals of the function $\frac{1}{\sin x\cos^3x}$

asked Dec 5, 2012 by sreemathi.v

1 answer

Find the integrals of the functions $\frac{\cos2x}{(\cos x+\sin x)^2}$

asked Dec 5, 2012 by sreemathi.v

1 answer

Find the integrals of the functions $\sin^{-1}(\cos x)$

asked Dec 5, 2012 by sreemathi.v

1 answer

Find the integrals of the functions $\frac{1}{\cos(x-a)\cos(x-b)}$

asked Dec 5, 2012 by sreemathi.v

1 answer

Choose the correct answer in $\Large \int \normalsize\frac{\large \sin^2x-\cos^2x}{\large \sin^2x\cos^2x}dx$ is equal to

asked Dec 5, 2012 by sreemathi.v

1 answer

$\Large \int \normalsize\frac{\large e^x(1+x)}{\large \cos^2(e^xx)}dx$ equals

asked Dec 5, 2012 by sreemathi.v

1 answer

Form a differential equation representing the given family of curves by eliminating arbitrary constants a and b $\large\frac{x}{a}+\frac{y}{b}=1$

asked Nov 30, 2012 by sreemathi.v

1 answer

Form a differential equation representing the given family of curves by eliminating arbitrary constants a and b.$y^2=a(b^2-x^2)$

asked Nov 30, 2012 by sreemathi.v

1 answer

Form a differential equation representing the given family of curves by eliminating arbitrary constants a and b. $y=a\: e^{3x}+b\: e^{-2x}$

asked Nov 30, 2012 by sreemathi.v

1 answer

Form a differential equation representing the given family of curves by eliminating arbitrary constants a and b $y=e^{2x}(a+bx)$

asked Nov 30, 2012 by sreemathi.v

1 answer

Form a differential equation representing the given family of curves by eliminating arbitrary constants a and b $y=e^x(a\;\cos x+b\;\sin x)$

asked Nov 30, 2012 by sreemathi.v

1 answer

Form the differential equation of the family of circles touching the \(y\) - axis at origin.

asked Nov 30, 2012 by sreemathi.v

1 answer

Form the differential equation of the family of parabolas having vertex at origin at axis along positive y-axis.

asked Nov 30, 2012 by sreemathi.v

1 answer

Form the differential equation of the family of ellipses having foci on $y$-axis and centre at origin.

asked Nov 30, 2012 by sreemathi.v

1 answer

Form the differential equation of the family of hyperbolas having foci on $x$-axis and centre at origin.

asked Nov 30, 2012 by sreemathi.v

1 answer

Form the differential equation of the family of circles having centre on $y$-axis and radius $3$ units.

asked Nov 30, 2012 by sreemathi.v

2 answers

Which of the following differential equations has $y\;=\;c_1e^x+c_2e^{-x}$ as the general solution?

asked Nov 30, 2012 by sreemathi.v

1 answer

Which of the following differential equations has $y = x$ as one of its particular solution?

asked Nov 30, 2012 by sreemathi.v

1 answer

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