List of top Mathematics Questions on types of vectors asked in KEAM

If $\vec{a} = 4\hat{i} + \lambda \hat{j} - 6\hat{k}$ and $\vec{b} = -6\hat{i} + 12\hat{j} + 9\hat{k}$ are collinear, then the value of $\lambda$ is equal to

If \(y = 4\sqrt{x}\) then \(\frac{d^2y}{dx^2} =\)

The unit vector in the direction of the vector \( \overrightarrow{AB} \) if \( A=(-2,-1,3) \) and \( B=(1,1,0) \) is \( \alpha i + \beta j + \gamma k \), then \( \alpha+\beta \) is

If $\vec{a} = 2\hat{i} - \hat{j} - m\hat{k}$ and $\vec{b} = \frac{4}{7}\hat{i} - \frac{2}{7}\hat{j} + 2\hat{k}$ are collinear, then the value of $m$ is equal to:

If the direction cosines of a vector of magnitude 3 are \( \frac{2}{3}, \frac{-a}{3}, \frac{2}{3} \), \( a > 0 \), then the vector is:

If the direction cosines of a vector of magnitude 3 are \( \frac{2}{3}, \frac{-a}{3}, \frac{2}{3} \), \( a > 0 \), then the vector is:

If the direction cosines of a vector of magnitude 3 are \( \frac{2}{3}, \frac{-a}{3}, \frac{2}{3} \), \( a > 0 \), then the vector is: