New chat PYQ Library Doubts Rank report

Sign in to see Recents

Sign in to save progress →

Vector Algebra question

2022 · 25 Jun · Shift 1 · Q40

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

PYQ Library
JEE Main
Mathematics
Vector Algebra
2022 · 25 Jun · Shift 1 · Q40

Vector Algebra question

2022 · 25 Jun · Shift 1 · Q40

JEE MainMathematicsVector AlgebraNumerical+4 / −1

Let

\theta

be the angle between the vectors

\overrightarrow a

and

\overrightarrow b

, where

|\overrightarrow a | = 4,|\overrightarrow b | = 3

and

\theta \in \left( {{\pi \over 4},{\pi \over 3}} \right)

. Then

{\left| {\left( {\overrightarrow a - \overrightarrow b } \right) \times \left( {\overrightarrow a + \overrightarrow b } \right)} \right|^2} + 4{\left( {\overrightarrow a \,.\,\overrightarrow b } \right)^2}

is equal to

\underline{\hspace{2cm}}

.

Numerical answer

More from Vector Algebra

Let $b = i + j + λ k$ , $λ \in$ R. If $a$ is a vector such that $a \times b = 13 i - j - 4 k$ and $a . b + 21 = 0$ …2022 · Numerical
Let $a = α \hat{i} + \hat{j} - \hat{k}$ and $b = 2 \hat{i} + \hat{j} - α \hat{k}, α > 0$ . If the projection of $a \times b$ …2022 · MCQ
Let $a = α \hat{i} + \hat{j} + β \hat{k}$ and $b = 3 \hat{i} - 5 \hat{j} + 4 \hat{k}$ be two vectors, such that $a \times b = - \hat{i} + 9 \hat{j} + 12 \hat{k}$ . Then the projection of $b - 2 a$ on $b + a$ …2022 · MCQ
Let $a$ , $b$ , $c$ be three non-coplanar vectors such that $a \times b$ = 4 $c$ , $b \times c$ = 9 $a$ …2022 · Numerical
Let $a = i + j - k$ and $c = 2 i - 3 j + 2 k$ . Then the number of vectors $b$ such that $b \times c = a$ …2022 · MCQ
Let $a$ and $b$ be the vectors along the diagonals of a parallelogram having area $22$ . Let the angle between $a$ and $b$ be acute, $∣ a ∣ = 1$ , and $∣ a . b ∣ = ∣ a \times b ∣$ …2022 · MCQ
Let the vectors $a = (1 + t) \hat{i} + (1 - t) \hat{j} + \hat{k}, b = (1 - t) \hat{i} + (1 + t) \hat{j} + 2 \hat{k}$ and $c = t \hat{i} - t \hat{j} + \hat{k}, t \in R$ be such that for $α, β, γ \in R, α a + β b + γ c = 0 \Rightarrow α = β = γ = 0$ …2022 · MCQ
Let a vector $a$ has magnitude 9. Let a vector $b$ be such that for every $(x, y) \in R \times R - {(0, 0)}$ , the vector $(x a + y b)$ is perpendicular to the vector $(6 y a - 18 x b)$ . Then…2022 · MCQ