If is the angle between any two vectors a and b , then | a b| = | a b| when is equal to 0 4 2

[Correct Option is b] As we know, | a b | = | a | | b | | | and | a b| = | a| b|| | We have, | a b| = | a b| | a | | b | | | = | a | | b | | | | | = | | | | = 1 = 1 = 4

Vector Algebra — Class 12 Maths Solution

ncert misc SA NCERT,Page 459,Misc,Q.No 19

Question

If $\theta$ is the angle between any two vectors $\vec a$ and $\vec b$, then $|\vec a \cdot \vec b| = |\vec a \times \vec b|$ when $\theta$ is equal to

•
• $0$

• $\cfrac{\pi }{4}$

• $\cfrac{\pi }{2}$

• $\pi$

Step-by-step Solution

[Correct Option is b]

As we know, $\left| {\vec a \cdot \vec b} \right| = \left| {\vec a} \right|\left| {\vec b} \right|\left| {\cos \theta } \right|$

and $|\vec a \times \vec b| = |\vec a|\vec b||\sin \theta |$

We have, $|\vec a \cdot \vec b| = |\vec a \times \vec b|$

$\Rightarrow \left| {\vec a} \right|\left| {\vec b} \right|\left| {\cos \theta } \right| = \left| {\vec a} \right|\left| {\vec b} \right|\left| {\sin \theta } \right|$

$\Rightarrow \tan \theta = 1 \Rightarrow \theta = \cfrac{\pi }{4}$

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NCERT & Exemplar solution for CBSE Class 12 Mathematics, Vector Algebra. Curated by Sachin Sharma. Free for all students.