1
JEE Main 2023 (Online) 24th January Evening Shift
+4
-1

Let $$\overrightarrow \alpha = 4\widehat i + 3\widehat j + 5\widehat k$$ and $$\overrightarrow \beta = \widehat i + 2\widehat j - 4\widehat k$$. Let $${\overrightarrow \beta _1}$$ be parallel to $$\overrightarrow \alpha$$ and $${\overrightarrow \beta _2}$$ be perpendicular to $$\overrightarrow \alpha$$. If $$\overrightarrow \beta = {\overrightarrow \beta _1} + {\overrightarrow \beta _2}$$, then the value of $$5{\overrightarrow \beta _2}\,.\left( {\widehat i + \widehat j + \widehat k} \right)$$ is :

A
9
B
7
C
6
D
11
2
JEE Main 2023 (Online) 24th January Morning Shift
+4
-1

Let PQR be a triangle. The points A, B and C are on the sides QR, RP and PQ respectively such that

$${{QA} \over {AR}} = {{RB} \over {BP}} = {{PC} \over {CQ}} = {1 \over 2}$$. Then $${{Area(\Delta PQR)} \over {Area(\Delta ABC)}}$$ is equal to :

A
$$\frac{5}{2}$$
B
4
C
2
D
3
3
JEE Main 2023 (Online) 24th January Morning Shift
+4
-1
Out of Syllabus

Let $$\overrightarrow u = \widehat i - \widehat j - 2\widehat k,\overrightarrow v = 2\widehat i + \widehat j - \widehat k,\overrightarrow v .\,\overrightarrow w = 2$$ and $$\overrightarrow v \times \overrightarrow w = \overrightarrow u + \lambda \overrightarrow v$$. Then $$\overrightarrow u .\,\overrightarrow w$$ is equal to :

A
$$- {2 \over 3}$$
B
$${3 \over 2}$$
C
2
D
1
4
JEE Main 2022 (Online) 29th July Evening Shift
+4
-1

Let $$\vec{a}, \vec{b}, \vec{c}$$ be three coplanar concurrent vectors such that angles between any two of them is same. If the product of their magnitudes is 14 and $$(\vec{a} \times \vec{b}) \cdot(\vec{b} \times \vec{c})+(\vec{b} \times \vec{c}) \cdot(\vec{c} \times \vec{a})+(\vec{c} \times \vec{a}) \cdot(\vec{a} \times \vec{b})=168$$, then $$|\vec{a}|+|\vec{b}|+|\vec{c}|$$ is equal to :

A
10
B
14
C
16
D
18
EXAM MAP
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