JEE MAIN - Physics (2021 - 22th July Evening Shift - No. 1)
What will be the projection of vector $$\overrightarrow A = \widehat i + \widehat j + \widehat k$$ on vector $$\overrightarrow B = \widehat i + \widehat j$$ ?
$$\sqrt 2 (\widehat i + \widehat j + \widehat k)$$
$$(\widehat i + \widehat j)$$
$$\sqrt 2 (\widehat i + \widehat j)$$
$$2(\widehat i + \widehat j + \widehat k)$$
Explanation
Projection = $${{\overrightarrow A .\overrightarrow B } \over {\left| {\overrightarrow B } \right|}}(\widehat B)$$
$$ = {{(\widehat i + \widehat j + \widehat k).(\widehat i + \widehat j)} \over {\sqrt 2 }}{{(\widehat i + \widehat j)} \over {\sqrt 2 }}$$
$$ = {2 \over {\sqrt 2 }} $$$$ \times $$$$ {{(\widehat i + \widehat j)} \over {\sqrt 2 }}$$
$$ = (\widehat i + \widehat j)$$
$$ = {{(\widehat i + \widehat j + \widehat k).(\widehat i + \widehat j)} \over {\sqrt 2 }}{{(\widehat i + \widehat j)} \over {\sqrt 2 }}$$
$$ = {2 \over {\sqrt 2 }} $$$$ \times $$$$ {{(\widehat i + \widehat j)} \over {\sqrt 2 }}$$
$$ = (\widehat i + \widehat j)$$
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