MCQ
$|a \times i{|^2} + |a \times j{|^2} + |a \times k{|^2} = $
- A$|a{|^2}$
- ✓$2\,\,|a{|^2}$
- C$3\,\,|a{|^2}$
- D$4\,\,|a{|^2}$
$ = \,|{a_3}j - {a_2}k{|^2} = a_3^2 + a_2^2$
Similarly, $|a \times j{|^2} = a_1^2 + a_3^2$ and $|a \times k{|^2} = a_1^2 + a_2^2$
Hence the required result can be given as
$2(a_1^2 + a_2^2 + a_3^2) = 2|a{|^2}.$
Generate a complete, print-ready paper with questions like this in minutes — across 16+ boards, with answer keys.
Let $x _1< x _2< x _3<\ldots< x _{ n }<\ldots$ be all the points of local maximum of $f$ and $y_1$
$(1)$ $\left|x_n-y_n\right|>1$ for every $n$
$(2)$ $x_1 < y _1$
$(3)$ $x_n \in\left(2 n , 2 n +\frac{1}{2}\right)$ for every $n$
$(4)$ $x_{n+1}-x_n>2$ for every $n$