Tag: vectors and transformations

Which will result in a vector?

What is the value of $p$ for which the vector $p\left( 2\hat { i } -\hat { j } +2\hat { k }  \right)$ is of $ 3$ units length?

If $\vec{x}$ and $\vec{y}$ be unit vectors and $\displaystyle |\vec{z}| = \dfrac{2}{\sqrt 7}$ such that $\vec{z} + (\vec{z} \times \vec{x}) = \vec{y}$ and $\theta$ is the angle between $\vec{x}$ and $\vec{z}$, then the value of sin $\theta$ is

If $\displaystyle a\times b=a\times c,a\neq 0,$ then

$\displaystyle a\times \left ( b+c \right )+b\times \left ( c+a \right )+c\times \left ( a+b \right )$ is equal to

Let $\displaystyle a=i+j$ and $\displaystyle b=2i-k,$ the point of intersection of the lines $\displaystyle r\times a=b\times a $ and $\displaystyle r\times b=a\times b $ is

If $\overline{a},\overline{b},\overline{c}$ are three non-zero vectors and $\overline{a}\neq\overline{b}$, $\overline{a}\times\overline{c}=\overline{b}\times\overline{c}$, then

If $a +2b +3c = 0$, then $a \times b + b\times c + c\times a = ka\times b,$
Where $k$ is equal to ?

If $\left| \vec { a }  \right| =1,\ \left| \vec { b }  \right| =2,\ (\vec { a },\vec { b })=\dfrac{2\pi}{3}$ then $\left{(\vec { a } +3\vec { b } )\times \left( 3\vec { a } -\vec { b }  \right) \right}^{2}=$

If $\vec a = \hat i + \hat j + \hat k,\,\vec b = \hat i + \hat j,\,\,\hat c = \hat i$ and $\left( {\vec a \times \vec b} \right) \times \vec c = \lambda \vec a \times \mu \vec b$ then $\lambda  + \mu $