List of top Mathematics Questions on Product of Two Vectors asked in AP EAMCET

A unit vector perpendicular to the vectors \( \bar{a} = 2\bar{i} + 3\bar{j} + 4\bar{k} \) and \( \bar{b} = 3\bar{j} + 2\bar{k} \) is:
The equation \( x^4 - x^3 - 6x^2 + 4x + 8 = 0 \) has two equal roots. If \( \alpha, \beta \) are the other two roots of this equation, then \( \alpha^2 + \beta^2 = \):
Two natural numbers are chosen at random from 1 to 100 and are multiplied. If \(A\) is the event that the product is an even number and \(B\) is the event that the product is divisible by 4, then \(P(A \cap \bar B) = \)
The vectors \(3\vec a-5\vec b\) and \(2\vec a+\vec b\) are mutually perpendicular and the vectors \(\vec a+4\vec b\) and \(-\vec a+\vec b\) are also mutually perpendicular. Then the acute angle between \(\vec a\) and \(\vec b\) is
If $a$ makes an acute angle with $b , r \cdot a =0$ and $r \times b = c \times b$, then $r =$