Eduprobe
Question:
Find |x⃗| if for a unit vector a⃗, (x⃗ - a⃗) . (x⃗ + a⃗) = 15
Solution:
Given: ||a⃗||=1
(x⃗ - a⃗) . (x⃗ + a⃗) = 15
We know that (a - b)(a + b) = a² - b²
So, ||x⃗||² - ||a⃗||² = 15
||x⃗||² - 1 = 15
||x⃗||² = 16
||x⃗|| = 4
Given: ||a⃗||=1
(x⃗ - a⃗) . (x⃗ + a⃗) = 15
We know that (a - b)(a + b) = a² - b²
So, ||x⃗||² - ||a⃗||² = 15
||x⃗||² - 1 = 15
||x⃗||² = 16
||x⃗|| = 4