Assertion -If a- - 2- - 3- - k- b- - - - 3- - 4k- then projection of a- on b- - 3-26- Reason- Projection of p- on q- - p- - q-q-

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Assertion :If...

Question

Assertion :If $\to a = 2^i + 3^j -^k, \to b = -^i + 3^j + 4^k$ then projection of $\to a$ on $\to b = \frac{3}{\sqrt{26}} .$ Reason: Projection of $¯ p$ on $¯ q = \frac{¯ p . ¯ q}{| ¯ q |}$ .

Both Assertion & Reason are individually true & Reason is correct explanation of Assertion

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Both Assertion & Reason are individually true but Reason is not the ,correct (proper) explanation of Assertion

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Assertion is true but Reason is false

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Assertion is false but Reason is true

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Solution

The correct option is A Both Assertion & Reason are individually true & Reason is correct explanation of Assertion
The projection of $¯ p$ on $¯ q$ is given by $\frac{¯ p . ¯ q}{| ¯ q |}$
For the given values, we have the projection as $\frac{- 2 + 9 - 4}{\sqrt{26}}$
i.e. $\frac{3}{\sqrt{26}}$
The correct option thus becomes $(A)$

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Assertion :If →a=2^i+3^j−^k,→b=−^i+3^j+4^k then projection of →a on →b=3√26. Reason: Projection of ¯p on ¯q=¯p.¯q|¯q|.

The correct option is A Both Assertion & Reason are individually true & Reason is correct explanation of AssertionThe projection of ¯p on ¯q is given by ¯p.¯q|¯q|For the given values, we have the projection as −2+9−4√26i.e. 3√26The correct option thus becomes (A)

Assertion :If $\to a = 2^i + 3^j -^k, \to b = -^i + 3^j + 4^k$ then projection of $\to a$ on $\to b = \frac{3}{\sqrt{26}} .$ Reason: Projection of $¯ p$ on $¯ q = \frac{¯ p . ¯ q}{| ¯ q |}$ .