Find the value of x for which x( i + j + k) is a unit vector.

Let us take a = x i + x j + x k . As we know, | a| = 1 + x 2 + x 2 = 1 3 x = 1 x = 3

Vector Algebra — Class 12 Maths Solution

ncert misc SA NCERT,Page 458,Misc,Q.No 5

Question

Find the value of $x$ for which $x(\hat i + \hat j + \hat k)$ is a unit vector.

Step-by-step Solution

Let us take $\vec a = x\hat i + x\hat j + x\hat k$. As we know, $|\vec a| = 1$

$\Rightarrow \sqrt {{x^2} + {x^2} + {x^2}} = 1 \Rightarrow \sqrt 3 x = \pm 1 \Rightarrow x = \pm \cfrac{1}{{\sqrt 3 }}$

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