The vectors a, b, c and d are such that a $$\times$$ b = c $$\times$$ d and a $$\times$$ c = b $$\times$$ d. Which of the following is/are correct?

1. (a $$-$$ d) $$\times$$ (b $$-$$ c) = 0

2. (a $$\times$$ b) $$\times$$ (c $$\times$$ d) = 0

Select the correct answer using the code given below.

Let $$a = \widehat i + \widehat j$$, $$b = 3\widehat i + 4\widehat k$$ and $$b = c + d$$, where c is parallel to a and d is perpendicular to a.

What is c equal to ?

Let $$a = \widehat i + \widehat j$$, $$b = 3\widehat i + 4\widehat k$$ and $$b = c + d$$, where c is parallel to a and d is perpendicular to a.

If $$d = x\widehat i + y\widehat j + z\widehat k$$, then which of the following equations is/are correct?

I. $$y - x = 4$$

II. $$2z - 3 = 0$$

Select the correct answer using the code given below.

Let a, b and c be three vectors such that a + b + c = 0 and | a | = 10, | b | = 6 and | c | = 14.

What is a . b + b . c + c . a equal to?