1
JEE Main 2024 (Online) 30th January Evening Shift
Numerical
+4
-1

A vector has magnitude same as that of $$\vec{A}=3 \hat{i}+4 \hat{j}$$ and is parallel to $$\vec{B}=4 \hat{i}+3 \hat{j}$$. The $$x$$ and $$y$$ components of this vector in first quadrant are $$x$$ and 3 respectively where $$x=$$ _________.

2
JEE Main 2023 (Online) 25th January Morning Shift
Numerical
+4
-1

If $$\overrightarrow P = 3\widehat i + \sqrt 3 \widehat j + 2\widehat k$$ and $$\overrightarrow Q = 4\widehat i + \sqrt 3 \widehat j + 2.5\widehat k$$ then, the unit vector in the direction of $$\overrightarrow P \times \overrightarrow Q$$ is $${1 \over x}\left( {\sqrt 3 \widehat i + \widehat j - 2\sqrt 3 \widehat k} \right)$$. The value of $$x$$ is _________.

3
JEE Main 2023 (Online) 24th January Morning Shift
Numerical
+4
-1

Vectors $$a\widehat i + b\widehat j + \widehat k$$ and $$2\widehat i - 3\widehat j + 4\widehat k$$ are perpendicular to each other when $$3a + 2b = 7$$, the ratio of $$a$$ to $$b$$ is $${x \over 2}$$. The value of $$x$$ is ____________.

4
JEE Main 2022 (Online) 28th July Morning Shift
Numerical
+4
-1

If the projection of $$2 \hat{i}+4 \hat{j}-2 \hat{k}$$ on $$\hat{i}+2 \hat{j}+\alpha \hat{k}$$ is zero. Then, the value of $$\alpha$$ will be ___________.