Let the vectors a and b be such that | a| = 3 and | b| = 3 , then a b is a unit vector, if the angle between a and b is /6 /4 /3 /2

Correct Option is b | a b| = | a|| b| 1 = (3) ( 3 ) = 2 = 4

Vector Algebra — Class 12 Maths Solution

ncert exercise SA NCERT,Page 454,Ex.10.4,Q.No 11

Question

Let the vectors $\vec a$ and $\vec b$ be such that $|\vec a| = 3$ and $|\vec b| = \cfrac{{\sqrt 2 }}{3}$, then $\vec a \times \vec b$ is a unit vector, if the angle between $\vec a$and $\vec b$ is

• $\pi /6$

• $\pi /4$

• $\pi /3$

• $\pi /2$

Step-by-step Solution

{Correct Option is b}

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

$\Rightarrow 1 = (3)\left( {\cfrac{{\sqrt 2 }}{3}} \right)\sin \theta \Rightarrow \sin \theta = \cfrac{1}{{\sqrt 2 }} \Rightarrow \theta = \cfrac{\pi }{4}$

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