Find the Angle Between the Vectors → a + → B and → a − → B If → a = 2 ˆ I − ˆ J + 3 ˆ K and → B = 3 ˆ I + ˆ J − 2 ˆ K , and Hence Find a Vector Perpendicular to Both → a + → B and → a − → B . - Mathematics

प्रश्न

Find the angle between the vectors $\vec{a} + \vec{b} and \vec{a} - \vec{b} if \vec{a} = 2 \hat{i} - \hat{j} + 3 \hat{k} and \vec{b} = 3 \hat{i} + \hat{j} - 2 \hat{k}, and hence find a vector perpendicular to both \vec{a} + \vec{b} and \vec{a} - \vec{b}$ .

योग

उत्तर

Here $\vec{a} + \vec{b} = 5 \hat{i} + \hat{k} and \vec{a} - \vec{b} = - \hat{i} - 2 \hat{j} + 5 \hat{k}$ .

Getting cos θ = 0

⇒ θ = $\frac{π}{2}$

a vector perpendicular to both $\vec{a} + \vec{b} and \vec{a} - \vec{b} is (\vec{a} + \vec{b}) \times (\vec{a} - \vec{b}) - 2 \hat{i} - 26 \hat{j} - 10 \hat{k}$ .

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Vectors Examples and Solutions

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Q 17 Q 16 Q 18

2015-2016 (March) All India Set 1 E

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2015-2016 (March) All India Set 1 E (with solutions)

Q 17 | 4 marks

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Find the Angle Between the Vectors → a + → B and → a − → B If → a = 2 ˆ I − ˆ J + 3 ˆ K and → B = 3 ˆ I + ˆ J − 2 ˆ K , and Hence Find a Vector Perpendicular to Both → a + → B and → a − → B . - Mathematics

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