1
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 ____________.

2
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 ___________.

3
JEE Main 2022 (Online) 26th July Evening Shift
Numerical
+4
-1

If $$\vec{A}=(2 \hat{i}+3 \hat{j}-\hat{k})\, \mathrm{m}$$ and $$\vec{B}=(\hat{i}+2 \hat{j}+2 \hat{k}) \,\mathrm{m}$$. The magnitude of component of vector $$\vec{A}$$ along vector $$\vec{B}$$ will be ____________ $$\mathrm{m}$$.

4
JEE Main 2021 (Online) 25th February Evening Shift
Numerical
+4
-1
If $$\overrightarrow P \times \overrightarrow Q = \overrightarrow Q \times \overrightarrow P$$, the angle between $$\overrightarrow P$$ and $$\overrightarrow Q$$ is $$\theta$$(0$$^\circ$$ < $$\theta$$ < 360$$^\circ$$). The value of '$$\theta$$' will be ___________$$^\circ$$.
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