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(B) Given that vector $b$ is in the north-east direction and vector $c$ is in the north-west direction. Since the angle between north-east and north-w

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$4\sqrt{2}$,towards west

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(B) Given that vector $b$ is in the north-east direction and vector $c$ is in the north-west direction. Since the angle between north-east and north-west is $90^\circ$,the vectors $b$ and $c$ are perpendicular,so $b \cdot c = 0$. Given $|b| = |c| = 4$. We need to find the magnitude and direction of $d = c - b$. The magnitude is given by $|d|^2 = |c - b|^2 = |c|^2 + |b|^2 - 2(b \cdot c)$. Substituting the values: $|d|^2 = 4^2 + 4^2 - 0 = 16 + 16 = 32$. Thus,$|d| = \sqrt{32} = 4\sqrt{2}$. Regarding the direction,since $c$ is at $135^\circ$ and $b$ is at $45^\circ$ from the positive $x$-axis (east),the vector $d = c - b$ points in the direction of the vector difference,which is towards the west.

The vectors $b$ and $c$ are in the direction of north-east and north-west respectively and $|b| = |c| = 4$. The magnitude and direction of the vector $d = c - b$ are:

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