New chat PYQ Library Doubts Rank report

Sign in to see Recents

Sign in to save progress →

Vector Algebra question

2025 · 28 Jan · Shift 2 · Q38

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

PYQ Library
JEE Main
Mathematics
Vector Algebra
2025 · 28 Jan · Shift 2 · Q38

Vector Algebra question

2025 · 28 Jan · Shift 2 · Q38

JEE MainMathematicsVector AlgebraMCQ+4 / −1

Let

A, B, C

be three points in xy-plane, whose position vector are given by

\sqrt{3} \hat{i}+\hat{j}, \hat{i}+\sqrt{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 from the line bisecting the angle between the vectors

\overrightarrow{\mathrm{OA}}

and

\overrightarrow{\mathrm{OB}}

is

\frac{9}{\sqrt{2}}

, then the sum of all the possible values of

a

is :

A
2
B
0
C
$\frac{9}{2}$
D
1

More from Vector Algebra

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
Let $\overset{a}{^}$ be a unit vector perpendicular to the vectors $b = \hat{i} - 2 \hat{j} + 3 \hat{k}$ and $c = 2 \hat{i} + 3 \hat{j} - \hat{k}$ , and $\overset{a}{^}$ makes an angle of $cos^{- 1} (- \frac{1}{3})$ with the vector $\hat{i} + \hat{j} + \hat{k}$ …2025 · MCQ
Let $a = - 5 \hat{i} + \hat{j} - 3 \hat{k}, b = \hat{i} + 2 \hat{j} - 4 \hat{k}$ and $c = (((a \times b) \times \hat{i}) \times \hat{i}) \times \hat{i}$ …2024 · MCQ
Let $a = \hat{i} + \hat{j} + \hat{k}, b = - \hat{i} - 8 \hat{j} + 2 \hat{k}$ and $c = 4 \hat{i} + c_{2} \hat{j} + c_{3} \hat{k}$ be three vectors such that $b \times a = c \times a$ …2024 · Numerical
Let a unit vector which makes an angle of $6 0^{\circ}$ with $2 \hat{i} + 2 \hat{j} - \hat{k}$ and an angle of $4 5^{\circ}$ with $\hat{i} - \hat{k}$ be $C$ . Then $C + (- \frac{1}{2} \hat{i} + \frac{1}{3 2} \hat{j} - \frac{2}{3} \hat{k})$ …2024 · MCQ
Let $ABC$ be a triangle of area $152$ and the vectors $AB = \hat{i} + 2 \hat{j} - 7 \hat{k}, BC = a \hat{i} + b \hat{j} + c \hat{k}$ and $AC = 6 \hat{i} + d \hat{j} - 2 \hat{k}, d > 0$ …2024 · Numerical
For $λ > 0$ , let $θ$ be the angle between the vectors $a = \hat{i} + λ \hat{j} - 3 \hat{k}$ and $b = 3 \hat{i} - \hat{j} + 2 \hat{k}$ . If the vectors $a + b$ and $a - b$ are mutually perpendicular,…2024 · MCQ