New chat PYQ Library Doubts Rank report

Sign in to see Recents

Sign in to save progress →

Vector Algebra question

2024 · 8 Apr · Shift 2 · Q44

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

PYQ Library
JEE Main
Mathematics
Vector Algebra
2024 · 8 Apr · Shift 2 · Q44

Vector Algebra question

2024 · 8 Apr · Shift 2 · Q44

JEE MainMathematicsVector AlgebraMCQ+4 / −1

Let

\overrightarrow{\mathrm{a}}=\hat{i}+2 \hat{j}+3 \hat{k}, \overrightarrow{\mathrm{b}}=2 \hat{i}+3 \hat{j}-5 \hat{k}

and

\overrightarrow{\mathrm{c}}=3 \hat{i}-\hat{j}+\lambda \hat{k}

be three vectors. Let

\overrightarrow{\mathrm{r}}

be a unit vector along

\vec{b}+\vec{c}

. If

\vec{r} \cdot \vec{a}=3

, then

3 \lambda

is equal to:

A
21
B
25
C
27
D
30

More from Vector Algebra

Let three vectors , $a = α \hat{i} + 4 \hat{j} + 2 \hat{k}, b = 5 \hat{i} + 3 \hat{j} + 4 \hat{k}, c = x \hat{i} + y \hat{j} + z \hat{k}$ form a triangle such that $c = a - b$ …2024 · MCQ
Let $O A = 2 a, O B = 6 a + 5 b$ and $O C = 3 b$ , where $O$ is the origin. If the area of the parallelogram with adjacent sides $O A$ and $O C$ …2024 · MCQ
Between the following two statements: Statement I : Let $a = \hat{i} + 2 \hat{j} - 3 \hat{k}$ and $b = 2 \hat{i} + \hat{j} - \hat{k}$ . Then the vector $r$ satisfying $a \times r = a \times b$ and $a \cdot r = 0$ …2024 · MCQ
Let $a = 2 \hat{i} + α \hat{j} + \hat{k}, b = - \hat{i} + \hat{k}, c = β \hat{j} - \hat{k}$ , where $α$ and $β$ are integers and $α β = - 6$ . Let the values of the ordered pair $(α, β)$ , for which the…2024 · MCQ
Let $a = \hat{i} + 2 \hat{j} + \hat{k}, b = 3 (\hat{i} - \hat{j} + \hat{k})$ . Let $c$ be the vector such that $a \times c = b$ …2024 · MCQ
The least positive integral value of $α$ , for which the angle between the vectors $α \hat{i} - 2 \hat{j} + 2 \hat{k}$ and $α \hat{i} + 2 α \hat{j} - 2 \hat{k}$ is acute, is .2024 · Numerical
Let the position vectors of the vertices $A, B$ and $C$ of a triangle be $2 \hat{i} + 2 \hat{j} + \hat{k}, \hat{i} + 2 \hat{j} + 2 \hat{k}$ and $2 \hat{i} + \hat{j} + 2 \hat{k}$ respectively. Let $l_{1}, l_{2}$ and $l_{3}$ be…2024 · MCQ
The position vectors of the vertices $A, B$ and $C$ of a triangle are $2 \hat{i} - 3 \hat{j} + 3 \hat{k}, 2 \hat{i} + 2 \hat{j} + 3 \hat{k}$ and $- \hat{i} + \hat{j} + 3 \hat{k}$ respectively. Let $l$ denotes the length of…2024 · MCQ