The angle between the vectors a + b and a -b, when a = (1, ,1, ,4… - Vidyadip

MCQ

The angle between the vectors $a + b$ and $a -b$, when $a = (1,\,1,\,4)$ and $b = (1,\, - 1,\,4)$ is .............. $^o$

✓
$90$
B
$45$
C
$30$
D
$15$

✓

Answer

Correct option: A.

$90$

a
(a) $a = (1,\,1,\,4) = i + j + 4k,$ $b = (1,\, - 1,\,4) = i - j + 4k$

$\therefore a + b = 2i + 8k$=> $a - b = 2j$

Since, $(a + b)\,.\,(a - b) = 0$

$\therefore (a + b) \bot (a - b)$. Hence $\theta = 90^\circ $.

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