List of top Mathematics Questions on Vector Algebra asked in BITSAT

What is the dot product of the vectors \( \mathbf{a} = (2, 3, 1) \) and \( \mathbf{b} = (1, -1, 4) \)?
Find the angle between the vectors \( \mathbf{a} = (2, 3, 1) \) and \( \mathbf{b} = (1, -1, 4) \).
Find the angle between the vectors \( \mathbf{a} = (2, -1, 3) \) and \( \mathbf{b} = (1, 4, -2) \).
The position of a projectile launched from the origin at $t=0$ is given by $\hat{r}=\left(40 \hat{i}+50\hat{ j}\right) m$ at $t=2 s$. If the projectile was launched at an angle $\theta$ from the horizontal, then $\theta$ is $\left(\right.$ take $\left. g=10\, ms ^{-2}\right)$
If $2 i + j - k$ and $i -4 j +\lambda k$ are perpendicular to each other, then $\lambda$ is equal to:
If the line (x-4)/(1)=(y-2)/(1)=(z-k)/(2) lies in the plane 2x-4y+z=7, then the value of k is
Area of the triangle formed by the line x+y=3 and angle bisectors of the pair of straight lines x²-y²+2y=1 is
A line segment has length 63 and direction ratios are 3,-2,6. If the line makes an obtuse angle with x-axis, the components of the line vector are