1
JEE Main 2023 (Online) 30th January Evening Shift
+4
-1
Out of Syllabus
Let $\lambda \in \mathbb{R}, \vec{a}=\lambda \hat{i}+2 \hat{j}-3 \hat{k}, \vec{b}=\hat{i}-\lambda \hat{j}+2 \hat{k}$.

If $((\vec{a}+\vec{b}) \times(\vec{a} \times \vec{b})) \times(\vec{a}-\vec{b})=8 \hat{i}-40 \hat{j}-24 \hat{k}$,

then $|\lambda(\vec{a}+\vec{b}) \times(\vec{a}-\vec{b})|^2$ is equal to :
A
136
B
140
C
144
D
132
2
JEE Main 2023 (Online) 30th January Evening Shift
+4
-1
Let $\vec{a}$ and $\vec{b}$ be two vectors, Let $|\vec{a}|=1,|\vec{b}|=4$ and $\vec{a} \cdot \vec{b}=2$. If $\vec{c}=(2 \vec{a} \times \vec{b})-3 \vec{b}$, then the value of $\vec{b} \cdot \vec{c}$ is :
A
$-48$
B
$-60$
C
$-84$
D
$-24$
3
JEE Main 2023 (Online) 30th January Morning Shift
+4
-1
Out of Syllabus

If $$\overrightarrow a ,\overrightarrow b ,\overrightarrow c$$ are three non-zero vectors and $$\widehat n$$ is a unit vector perpendicular to $$\overrightarrow c$$ such that $$\overrightarrow a = \alpha \overrightarrow b - \widehat n,(\alpha \ne 0)$$ and $$\overrightarrow b \,.\overrightarrow c = 12$$, then $$\left| {\overrightarrow c \times (\overrightarrow a \times \overrightarrow b )} \right|$$ is equal to :

A
15
B
9
C
6
D
12
4
JEE Main 2023 (Online) 30th January Morning Shift
+4
-1

Let a unit vector $$\widehat{O P}$$ make angles $$\alpha, \beta, \gamma$$ with the positive directions of the co-ordinate axes $$\mathrm{OX}$$, $$\mathrm{OY}, \mathrm{OZ}$$ respectively, where $$\beta \in\left(0, \frac{\pi}{2}\right)$$. If $$\widehat{\mathrm{OP}}$$ is perpendicular to the plane through points $$(1,2,3),(2,3,4)$$ and $$(1,5,7)$$, then which one of the following is true?

A
$$\alpha \in\left(\frac{\pi}{2}, \pi\right)$$ and $$\gamma \in\left(\frac{\pi}{2}, \pi\right)$$
B
$$\alpha \in\left(0, \frac{\pi}{2}\right)$$ and $$\gamma \in\left(\frac{\pi}{2}, \pi\right)$$
C
$$\alpha \in\left(\frac{\pi}{2}, \pi\right)$$ and $$\gamma \in\left(0, \frac{\pi}{2}\right)$$
D
$$\alpha \in\left(0, \frac{\pi}{2}\right)$$ and $$\gamma \in\left(0, \frac{\pi}{2}\right)$$
EXAM MAP
Medical
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