Find a unit vector in the direction of \(\overrightarrow { a } =3\overrightarrow { i } -2\overrightarrow { j } +6\overrightarrow { k } \)

For what value of \(\lambda\) are the vectors \(\overrightarrow { a } =2\overrightarrow { i } +\lambda \overrightarrow { j } +\overrightarrow { k } \) and \(\overrightarrow { b } =\overrightarrow { i } -2\overrightarrow { j } +3\overrightarrow { k } \)  perpendicular to each other?

If \(\overrightarrow { a } =\overrightarrow { i } +2\overrightarrow { j } -\overrightarrow { k } \ and\ \overrightarrow { b } =3\overrightarrow { i } +\overrightarrow { j } -5\overrightarrow { k } \) find a unit vector in the direction of \(\overrightarrow { a } -\overrightarrow { b } \)

If \(\left| \overrightarrow { a } \right| =2,\left| \overrightarrow { b } \right| =\sqrt { 3 } \)  and \(\overrightarrow { a } .\overrightarrow { b } =\sqrt { 3 } \) find the angle between \(\overrightarrow { a } \ and\ \overrightarrow { b } \)

If \(\overrightarrow { a } =\hat { i } +2\hat { j } -3\hat { k } \) and \(\overrightarrow { b } =2\hat { i } +4\hat { j } +9\hat { k } \) find a unit vector parallel to \(\overrightarrow { a } +\overrightarrow { b } \)

If \(\left| \overrightarrow { a } \right| =\sqrt { 3 } ,\left| \overrightarrow { b } \right| =2\) and angle between \(\overrightarrow { a } \ and\ \overrightarrow { b } \) is 60^o find \(\overrightarrow { a } .\overrightarrow { b } \)

Find a vector in the direction of \(\overrightarrow { a } =\overrightarrow { i } -2\overrightarrow { j } \) whose magnitude is 7.

Find the projection of \(\overrightarrow { a } \ on\ \overrightarrow { b } \) if \(\overrightarrow { a } .\overrightarrow { b } =8\ and\ \overrightarrow { b } =2\overrightarrow { i } +6\overrightarrow { j } +3\overrightarrow { k } \)

Write the value of p for which \(\overrightarrow { a } =3\hat { i } +2\hat { j } +9\hat { k } \quad and\quad \overrightarrow { b } =\hat { i } +p\hat { j } +3\hat { k } \)  are parallel vectors.

For any two vectors \(\vec{a} \text { and } \vec{b}\)
\(\vec{a}+\vec{b}=\vec{b}+\vec{a}\) (Commutative property)