Let a = 2i - 7j + 5k, b = i + k and c = i + 2j - 3k be three given vectors.

Question

Let \(\vec a = 2\hat i - 7\hat j + 5\hat k, \vec b = \hat i + \hat k\) and \(\vec c = \hat i + 2\hat j - 3\hat k\) be three given vectors. If \(\vec r\) is a vector such that \(\vec r \times \vec a = \vec c \times \vec a\) and \(\vec r.\vec b = 0\), then \(|\vec r|\) is equal to:

(1) \(\frac{11}7 \sqrt{2}\)

(2) \(\frac{11}7 \)

(3) \(\frac{11}5 \sqrt{2}\)

(4) \(\frac{\sqrt{914}}7\)

Answer 1

Correct option is (1) \(\frac{11}7 \sqrt{2}\)