New chat PYQ Library Doubts Rank report

Sign in to see Recents

Sign in to save progress →

Vector Algebra question

2025 · 7 Apr · Shift 1 · Q44

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

PYQ Library
JEE Main
Mathematics
Vector Algebra
2025 · 7 Apr · Shift 1 · Q44

Vector Algebra question

2025 · 7 Apr · Shift 1 · Q44

JEE MainMathematicsVector AlgebraMCQ+4 / −1

Let the angle

\theta, 0\lt \theta\lt \frac{\pi}{2}

between two unit vectors

\hat{a}

and

\hat{b}

be

\sin ^{-1}\left(\frac{\sqrt{65}}{9}\right)

. If the vector

\vec{c}=3 \hat{a}+6 \hat{b}+9(\hat{a} \times \hat{b})

, then the value of

9(\vec{c} \cdot \hat{a})-3(\vec{c} \cdot \hat{b})

is

A
31
B
29
C
24
D
27

More from Vector Algebra

Let $a$ and $b$ be the vectors of the same magnitude such that $\frac{∣ a + b ∣ + ∣ a - b ∣}{∣ a + b ∣ - ∣ a - b ∣} = 2 + 1.$ Then $\frac{∣ a + b ∣ ^{2}}{∣ a ∣ ^{2}}$ is :2025 · MCQ
Let $a = \hat{i} + 2 \hat{j} + \hat{k}$ and $b = 2 \hat{i} + \hat{j} - \hat{k}$ . Let $\overset{c}{^}$ be a unit vector in the plane of the vectors $a$ and $b$ and be perpendicular to $a$ . Then such a vector $\overset{c}{^}$ …2025 · MCQ
Let $c$ be the projection vector of $b = λ \hat{i} + 4 \hat{k}, λ > 0$ , on the vector $a = \hat{i} + 2 \hat{j} + 2 \hat{k}$ . If $∣ a + c ∣ = 7$ , then the area of the parallelogram formed by the vectors $b$ …2025 · Numerical
Let $a$ and $b$ be two unit vectors such that the angle between them is $\frac{π}{3}$ . If $λ a + 2 b$ and $3 a - λ b$ are perpendicular to each other, then the number of values of $λ$ in $[- 1, 3]$ …2025 · MCQ
Let the position vectors of the vertices $A, B$ and C of a tetrahedron ABCD be $\hat{i} + 2 \hat{j} + \hat{k}, \hat{i} + 3 \hat{j} - 2 \hat{k}$ and $2 \hat{i} + \hat{j} - \hat{k}$ …2025 · MCQ
Let the arc $B$ of a circle subtend a right angle at the centre $O$ . If the point $A C$ on the arc $A C$ , divides the arc $A C$ such that $\frac{length of arc A B}{length of arc B C} = \frac{1}{5}$ …2025 · MCQ
Let the point A divide the line segment joining the points $P (- 1, - 1, 2)$ and $Q (5, 5, 10)$ internally in the ratio $r : 1 (r > 0)$ . If O is the origin and $(OQ \cdot OA) - \frac{1}{5} ∣ OP \times OA ∣^{2} = 10$ …2025 · MCQ
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