Question

The two vectors a=2i + j + 3k and b=7i - 5j - 3k are

Answer 1

The two vectors A=2i +j+2k and B=7i - 5j- 3k are

A) Parallel

B) Perpendicular

C) Anti-parallel

D) None of these

answer : (B)

solution : two vectors A and B will be parallel only if it is resolved as A = kB, where k is positive real numbers.

and A and B are antiparallel only if it is resolved as A = kB, where k is negativereal numbers.

here, 2i + j + 3k ≠ (7i - 5j - 3k)

so, a and b are neither parallel nor antiparallel.

now, we know, two vectors A and B are perpendicular to each other when dot product of A and B , A.B = 0

here, a.b = (2i + j + 3k).(7i - 5j - 3k)

= 14 - 5 - 9 = 14 - 14 = 0

hence, a and b are perpendicular to each other.

hence, option (B) is correct choice.

Answer 2

Answer:

The answer is option B) perpendicular