New chat PYQ Library Doubts Rank report

Sign in to see Recents

Sign in to save progress →

Vector Algebra question

2025 · 29 Jan · Shift 1 · Q41

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

PYQ Library
JEE Main
Mathematics
Vector Algebra
2025 · 29 Jan · Shift 1 · Q41

Vector Algebra question

2025 · 29 Jan · Shift 1 · Q41

JEE MainMathematicsVector AlgebraMCQ+4 / −1

Let

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

and

\vec{c}

be a vector such that

\vec{a} \times \vec{c} = \vec{a} \times \vec{b} = \vec{c} \times \vec{b}

and

(\vec{a} + \vec{c}) \cdot (\vec{b} + \vec{c}) = 168

. Then the maximum value of

|\vec{c}|^2

is :

A
77
B
154
C
308
D
462

More from Vector Algebra

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
Let $a = \hat{i} + \hat{j} + \hat{k}, b = 2 \hat{i} + 4 \hat{j} - 5 \hat{k}$ and $c = x \hat{i} + 2 \hat{j} + 3 \hat{k}, x \in R$ . If $d$ is the unit vector in the direction of $b + c$ such that $a \cdot d = 1$ …2024 · MCQ
If $A (1, - 1, 2), B (5, 7, - 6), C (3, 4, - 10)$ and $D (- 1, - 4, - 2)$ are the vertices of a quadrilateral ABCD, then its area is :2024 · MCQ