If a is a non-zero vector of magnitude 'a' and a non- zero scalar, then a is unit vector if = 1 = - 1 a = | | a = 1/| |

Option d is Correct a is a non-zero vector of magnitude a | a| = a Since a is a unit vector | a| = 1 | || a| = 1 | |a = 1 a = | | Exercise-10.4

Vector Algebra — Class 12 Maths Solution

ncert exercise SA NCERT,Page 448,Ex.10.3,Q.No 18

Question

If $\vec a$ is a non-zero vector of magnitude $'a'$ and $\lambda$ a non- zero scalar, then $\lambda \vec a$ is unit vector if

• $\lambda = 1$

• $\lambda = - 1$

• $a = |\lambda |$

• $a = 1/|\lambda |$

Step-by-step Solution

{Option d is Correct}

$\vec a$ is a non-zero vector of magnitude $a \Rightarrow |\vec a| = a$
Since $\lambda \vec a$ is a unit vector

$\Rightarrow |\lambda \vec a| = 1 \Rightarrow |\lambda ||\vec a| = 1 \Rightarrow |\lambda |a = 1$
$\Rightarrow a = \cfrac{1}{{|\lambda |}}$

Exercise-10.4

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