1
JEE Main 2023 (Online) 31st January Morning Shift
MCQ (Single Correct Answer)
+4
-1

Let $$\vec{a}=2 \hat{i}+\hat{j}+\hat{k}$$, and $$\vec{b}$$ and $$\vec{c}$$ be two nonzero vectors such that $$|\vec{a}+\vec{b}+\vec{c}|=|\vec{a}+\vec{b}-\vec{c}|$$ and $$\vec{b} \cdot \vec{c}=0$$. Consider the following two statements:

(A) $$|\vec{a}+\lambda \vec{c}| \geq|\vec{a}|$$ for all $$\lambda \in \mathbb{R}$$.

(B) $$\vec{a}$$ and $$\vec{c}$$ are always parallel.

Then,

A
only (B) is correct
B
both (A) and (B) are correct
C
only (A) is correct
D
neither (A) nor (B) is correct
2
JEE Main 2023 (Online) 30th January Evening Shift
MCQ (Single Correct Answer)
+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
3
JEE Main 2023 (Online) 30th January Evening Shift
MCQ (Single Correct Answer)
+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
$-24$
4
JEE Main 2023 (Online) 30th January Morning Shift
MCQ (Single Correct Answer)
+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
EXAM MAP
Medical
NEET
Graduate Aptitude Test in Engineering
GATE CSEGATE ECEGATE EEGATE MEGATE CEGATE PIGATE IN
Civil Services
UPSC Civil Service
Defence
NDA
CBSE
Class 12