Vectors

The vectors a and b are not perpendicular

The vectors a and b are not perpendicular and c and d are two vectors satisfying: b x c = b x d and a.d = 0. Then the vector d is equal to

b - (b.c/a.d)c
c + (a.c/a.b)b
c - (a.c/a.b)b
b - (b.c/a.d)c

If the vectors a = i-j+2k, b = 2i+4j+k and c = ai+j+bk

If the vectors a = i - j + 2k, b = 2i + 4j + k and c = ai + j + bk are mutually orthogonal, then (a,b) =

(-2,3)
(3,-2)
(-3,2)
(2,-3)

Let a = j - k and c = i - j - k. Then the vector b satisfying a x b + c = 0 and a.b = 3 is

Let a = j - k and c = i - j - k. Then the vector b satisfying a x b + c = 0 and a.b = 3 is

i - j - 2k
i + j - 2k
2i - j + 2k
-i + j - 2k

If |a| = 4, |b| = 2 and the angle between a and b is π/6

If |a| = 4, |b| = 2 and the angle between a and b is π/6, then (a × b)² is equal to

14
16
36
48

a, b and c are 3 vectors, such that a + b + c = 0, |a| = 1, |b| = 2|c|

a, b and c are 3 vectors, such that a + b + c = 0, |a| = 1, |b| = 2|c|, then a.b + b.c + c.a is equal to

1
0
-7
7

Let a and b be two unit vectors. If the vectors c = a + 2b and d = 5a - 4b

Let a and b be two unit vectors. If the vectors c = a + 2b and d = 5a - 4b are perpendicular to each other, then the angle between a and b is

π/4
π/6
π/2
π/3