New chat PYQ Library Doubts Rank report

Sign in to see Recents

Sign in to save progress →

Vector Algebra question

2025 · 23 Jan · Shift 2 · Q29

Guest · try one question or challengeGuest · try one question or challenge

PYQ Library
JEE Main
Mathematics
Vector Algebra
2025 · 23 Jan · Shift 2 · Q29

Vector Algebra question

2025 · 23 Jan · Shift 2 · Q29

JEE MainMathematicsVector AlgebraMCQ+4 / −1

Let the point A divide the line segment joining the points

\mathrm{P}(-1,-1,2)

and

\mathrm{Q}(5,5,10)

internally in the ratio

r: 1(r\gt 0)

. If O is the origin and

(\overrightarrow{\mathrm{OQ}} \cdot \overrightarrow{\mathrm{OA}})-\frac{1}{5}|\overrightarrow{\mathrm{OP}} \times \overrightarrow{\mathrm{OA}}|^2=10

, then the value of r is :

A
$\sqrt7$
B
14
C
7
D
3

More from Vector Algebra

Let $a = \hat{i} + 2 \hat{j} + 3 \hat{k}, b = 3 \hat{i} + \hat{j} - \hat{k}$ and $c$ be three vectors such that $c$ is coplanar with $a$ and $b$ . If the vector $C$ is perpendicular to $b$ and $a \cdot c = 5$ …2025 · MCQ
Let the position vectors of three vertices of a triangle be $4 p + q - 3 r, - 5 p + q + 2 r$ and $2 p - q + 2 r$ . If the position vectors of the orthocenter and the circumcenter of the triangle are $\frac{p + q + r}{4}$ …2025 · MCQ
Let $a = 3 \hat{i} - \hat{j} + 2 \hat{k}, b = a \times (\hat{i} - 2 \hat{k})$ and $c = b \times \hat{k}$ . Then the…2025 · MCQ
Let $a = \hat{i} + \hat{j} + \hat{k}, b = 2 \hat{i} + 2 \hat{j} + \hat{k}$ and $d = a \times b$ . If $c$ …2025 · Numerical
If the components of $a = α \hat{i} + β \hat{j} + γ \hat{k}$ along and perpendicular to $b = 3 \hat{i} + \hat{j} - \hat{k}$ respectively, are $\frac{16}{11} (3 \hat{i} + \hat{j} - \hat{k})$ and $\frac{1}{11} (- 4 \hat{i} - 5 \hat{j} - 17 \hat{k})$ …2025 · MCQ
Let $A, B, C$ be three points in xy-plane, whose position vector are given by $3 \hat{i} + \hat{j}, \hat{i} + 3 \hat{j}$ and $a \hat{i} + (1 - a) \hat{j}$ respectively with respect to the origin O . If the distance of the point C…2025 · MCQ
Let $a = \hat{i} + 2 \hat{j} + \hat{k}$ and $b = 2 \hat{i} + 7 \hat{j} + 3 \hat{k}$ . Let $L_{1} : r = (- \hat{i} + 2 \hat{j} + \hat{k}) + λ a, λ \in R$ and $L_{2} : r = (\hat{j} + \hat{k}) + μ b, μ \in R$ …2025 · MCQ
Let $a = 2 \hat{i} - \hat{j} + 3 \hat{k}, b = 3 \hat{i} - 5 \hat{j} + \hat{k}$ and $c$ be a vector such that $a \times c = a \times b = c \times b$ and $(a + c) \cdot (b + c) = 168$ …2025 · MCQ