List of top Mathematics Questions on Section Formula asked in KEAM

The position vectors of the points $A$ and $B$ are $\vec{a} = 2\hat{i} - \lambda \hat{j} + 5\hat{k}$ and $\vec{b} = \mu \hat{i} + 7\hat{j} + 3\hat{k}$ respectively. If the position vector of the mid-point of the line segment $AB$ is $\vec{c} = 3\hat{i} + 2\hat{j} + 4\hat{k}$, then the value of $\lambda + \mu$ is equal to

If the position vectors of the points P and Q are, respectively, \(5\vec{a} - 6\vec{b}\) and \(\vec{a} + 2\vec{b}\), then the point R with position vector \(2\vec{a}\) divides the line segment joining P and Q internally in the ratio

Let $O$ be the origin. Let $\overrightarrow{OA} = \vec{a}$ and $\overrightarrow{OB} = \vec{b}$ be the position vectors of the points $A$ and $B$ respectively. A point $P$ divides the line segment $AB$ internally in the ratio $m:n$. Then $\overrightarrow{AP}$ is equal to:

Let $P(1,2)$, $Q(a,b)$, $R(5,7)$ and $S(2,3)$ be the vertices of a parallelogram $PQRS$. Then ________.

The coordinate of the point dividing internally the line joining the points \( (4,-2) \) and \( (8,6) \) in the ratio \( 7:5 \) is

The coordinate of the point dividing internally the line joining the points \( (4,-2) \) and \( (8,6) \) in the ratio \( 7:5 \) is

The coordinate of the point dividing internally the line joining the points \( (4,-2) \) and \( (8,6) \) in the ratio \( 7:5 \) is

The ratio by which the line \( 2x + 5y - 7 = 0 \) divides the straight line joining the points \( (-4, 7) \) and \( (6, -5) \) is:

The ratio by which the line \( 2x + 5y - 7 = 0 \) divides the straight line joining the points \( (-4, 7) \) and \( (6, -5) \) is:

The ratio by which the line \( 2x + 5y - 7 = 0 \) divides the straight line joining the points \( (-4, 7) \) and \( (6, -5) \) is: