The sides of a parallelogram are 2 i+4 j-5 k and i+2 j+3 k. The unit vector parallel to one of the diagonals size is

Question

The sides of a parallelogram are 2 i+4 j-5 k and i+2 j+3 k. The unit vector parallel to one of the diagonals size is (A) (1/7)(3 i+6 j-2 k) (B) (1/7)(3 i-6 j-2 k) (C) (1/7)(-3 i+6 j-2 k) (D) (1/7)(3 i+6 j+2 k)

Tardigrade Admin · Accepted Answer

Let a=2 i+4 j-5 k, b=i+2 j+3 k ∴ diagonals of the parallelogram are p=a+b and q=b-a i.e., p=3 i+6 j-2 k and, q=-i-2 j+8 k ∴ unit vectors along the diagonals are (3 i+6 j-2 k/√9+36+4) and (-i-2 j+8 k/√1+4+64) i.e., (3 i+6 j-2 k/7) and (-i-2 j+8 k/√69) ∴ unit vector parallel to one of the diagonals is (1/7)(3 i+6 j-2 k)

Q. The sides of a parallelogram are $2 i + 4 j - 5 k$ and $i + 2 j + 3 k$ . The unit vector parallel to one of the diagonals size is

$\frac{1}{7} (3 i + 6 j - 2 k)$

$\frac{1}{7} (3 i - 6 j - 2 k)$

$\frac{1}{7} (- 3 i + 6 j - 2 k)$

$\frac{1}{7} (3 i + 6 j + 2 k)$

Q. The sides of a parallelogram are 2i+4j−5k and i+2j+3k. The unit vector parallel to one of the diagonals size is

71​(3i+6j−2k)

71​(3i−6j−2k)

71​(−3i+6j−2k)

71​(3i+6j+2k)

Q. The sides of a parallelogram are $2 i + 4 j - 5 k$ and $i + 2 j + 3 k$ . The unit vector parallel to one of the diagonals size is

$\frac{1}{7} (3 i + 6 j - 2 k)$

$\frac{1}{7} (3 i - 6 j - 2 k)$

$\frac{1}{7} (- 3 i + 6 j - 2 k)$

$\frac{1}{7} (3 i + 6 j + 2 k)$