1
COMEDK 2021
+1
-0

If |a| = 8, |b| = 3 and |a $$\times$$ b| = 12, then find the angle between a and b.

A
$$\frac{\pi}{3}$$
B
$$\frac{\pi}{6}$$
C
$$\frac{\pi}{4}$$
D
None of these
2
COMEDK 2021
+1
-0

If for $$a = 2\widehat i + 3\widehat j + \widehat k,b = \widehat i - 2\widehat j + \widehat k$$ and $$c = - 3\widehat i + \widehat j + 2\widehat k$$, then find $$[a\,b\,c]$$.

A
$$-15$$
B
$$-10$$
C
$$-30$$
D
$$-5$$
3
COMEDK 2020
+1
-0

If a and b are vectors such that $$|a + b|=|a-b|$$, then the angle between a and b is

A
60$$^\circ$$
B
120$$^\circ$$
C
30$$^\circ$$
D
90$$^\circ$$
4
COMEDK 2020
+1
-0

If $$a = 2\widehat i + 3\widehat j - \widehat k,b = \widehat i + 2\widehat j - 5\widehat k,c = 3\widehat i + 5\widehat j - \widehat k$$, then a vector perpendicular to a and in the plane containing b and c is

A
$$17\widehat i + 21\widehat j - 123\widehat k$$
B
$$- 17\widehat i + 21\widehat j - 97\widehat k$$
C
$$- 17\widehat i - 21\widehat j - 97\widehat k$$
D
$$- 17\widehat i - 21\widehat j + 97\widehat k$$
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