Mathemerize

Let \(\vec{a}\), \(\vec{b}\), \(\vec{c}\) be three vectors. Then the scalar \((\vec{a}\times \vec{b}).\vec{c}\) is called the scalar triple product of \(\vec{a}\), \(\vec{b}\) and \(\vec{c}\) and is denoted by [\(\vec{a}\) \(\vec{b}\) \(\vec{c}\)]. Thus, we have  [\(\vec{a}\) \(\vec{b}\) \(\vec{c}\)] = \((\vec{a}\times \vec{b}).\vec{c}\) For three vectors \(\vec{a}\), \(\vec{b}\) & \(\vec{c}\), it is also defined as : (\(\vec{a}\times\vec{b}\)).\(\vec{c}\) = \(|\vec{a}||\vec{b}||\vec{c}|sin\theta …

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Let \(\vec{a}\) and \(\vec{b}\) be two non-zero vectors inclined at an angle \(\theta\). Then the scalar product or dot product of two vectors, \(\vec{a}\) with \(\vec{b}\) is denoted by \(\vec{a}\).\(\vec{b}\) and is defined as, \(\vec{a}\).\(\vec{b}\) = \(|\vec{a}||\vec{b}|cos\theta\)  If \(\vec{a}\) = \(a_1\hat{i}+a_2\hat{j}+a_3\hat{k}\) and \(\vec{b}\) = \(b_1\hat{i}+b_2\hat{j}+b_3\hat{k}\). Then \(\vec{a}\).\(\vec{b}\) = \(a_1b_1+a_2b_2+c_1c_2\) Properties of Dot Product of Two …

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Cross Product of Vectors Formula : Let \(\vec{a}\) & \(\vec{b}\) are two vectors & \(\theta\) is the angle between them, then cross product of vectors formula is, \(\vec{a}\) \(\times\) \(\vec{b}\) = |\(\vec{a}\)||\(\vec{b}\)|sin\(\theta\)\(\hat{n}\) where \(\hat{n}\) is the unit vector perpendicular to both \(\vec{a}\) & \(\vec{b}\). Properties of Vector Cross Product : (i) \(\vec{a}\) \(\times\) \(\vec{b}\) = …

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