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Mathematics
If \[\vec{a} \text{ and } \vec{b}\] are two vectors such that \[\left| \vec{a} \right| = 4, \left| \vec{b} \right| = 3 \text{ and } \vec{a} \cdot \vec{b} = 6\] find the angle between \[\vec{a} \text{ and } \vec{b} .\]
Chapter: [10] Vectors
Concept: undefined >> undefined
Concept: undefined >> undefined
\[\text{ If } \vec{a} = \hat{i} - \hat{j} \text{ and } \vec{b} = - \hat{j} + 2\hat{k} , \text{find} \left( \vec{a} - 2 \vec{b} \right) \cdot \left( \vec{a} + \vec{b} \right) .\]
Chapter: [10] Vectors
Concept: undefined >> undefined
Concept: undefined >> undefined
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\[\int\limits_4^9 \frac{1}{\sqrt{x}} dx\]
Chapter: [7] Integrals
Concept: undefined >> undefined
Concept: undefined >> undefined
\[\int\limits_{- 2}^3 \frac{1}{x + 7} dx\]
Chapter: [7] Integrals
Concept: undefined >> undefined
Concept: undefined >> undefined
\[\int\limits_0^{1/2} \frac{1}{\sqrt{1 - x^2}} dx\]
Chapter: [7] Integrals
Concept: undefined >> undefined
Concept: undefined >> undefined
\[\int\limits_0^1 \frac{1}{1 + x^2} dx\]
Chapter: [7] Integrals
Concept: undefined >> undefined
Concept: undefined >> undefined
\[\int\limits_2^3 \frac{x}{x^2 + 1} dx\]
Chapter: [7] Integrals
Concept: undefined >> undefined
Concept: undefined >> undefined
\[\int\limits_0^\infty \frac{1}{a^2 + b^2 x^2} dx\]
Chapter: [7] Integrals
Concept: undefined >> undefined
Concept: undefined >> undefined
\[\int\limits_{- 1}^1 \frac{1}{1 + x^2} dx\]
Chapter: [7] Integrals
Concept: undefined >> undefined
Concept: undefined >> undefined
\[\int\limits_0^\infty e^{- x} dx\]
Chapter: [7] Integrals
Concept: undefined >> undefined
Concept: undefined >> undefined
\[\int\limits_0^1 \frac{x}{x + 1} dx\]
Chapter: [7] Integrals
Concept: undefined >> undefined
Concept: undefined >> undefined
\[\int\limits_0^{\pi/2} \left( \sin x + \cos x \right) dx\]
Chapter: [7] Integrals
Concept: undefined >> undefined
Concept: undefined >> undefined
\[\int\limits_{\pi/4}^{\pi/2} \cot x\ dx\]
Chapter: [7] Integrals
Concept: undefined >> undefined
Concept: undefined >> undefined
\[\int\limits_0^{\pi/4} \sec x dx\]
Chapter: [7] Integrals
Concept: undefined >> undefined
Concept: undefined >> undefined
\[\int\limits_{\pi/6}^{\pi/4} cosec\ x\ dx\]
Chapter: [7] Integrals
Concept: undefined >> undefined
Concept: undefined >> undefined
\[\int\limits_0^1 \frac{1 - x}{1 + x} dx\]
Chapter: [7] Integrals
Concept: undefined >> undefined
Concept: undefined >> undefined
\[\int\limits_0^\pi \frac{1}{1 + \sin x} dx\]
Chapter: [7] Integrals
Concept: undefined >> undefined
Concept: undefined >> undefined
\[\int\limits_{- \pi/4}^{\pi/4} \frac{1}{1 + \sin x} dx\]
Chapter: [7] Integrals
Concept: undefined >> undefined
Concept: undefined >> undefined
\[\int\limits_0^{\pi/2} \cos^2 x\ dx\]
Chapter: [7] Integrals
Concept: undefined >> undefined
Concept: undefined >> undefined
\[\int\limits_0^{\pi/2} \cos^3 x\ dx\]
Chapter: [7] Integrals
Concept: undefined >> undefined
Concept: undefined >> undefined
