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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 ___________.

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2
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 ____________ $$\mathrm{m}$$.

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3
JEE Main 2021 (Online) 22th July Evening Shift
Numerical
+4
-1
Three particles P, Q and R are moving along the vectors $$\overrightarrow A = \widehat i + \widehat j$$, $$\overrightarrow B = \widehat j + \widehat k$$ and $$\overrightarrow C = - \widehat i + \widehat j$$ respectively. They strike on a point and start to move in different directions. Now particle P is moving normal to the plane which contains vector $$\overrightarrow A $$ and $$\overrightarrow B $$. Similarly particle Q is moving normal to the plane which contains vector $$\overrightarrow A $$ and $$\overrightarrow C $$. The angle between the direction of motion of P and Q is $${\cos ^{ - 1}}\left( {{1 \over {\sqrt x }}} \right)$$. Then the value of x is _______________.
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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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