The sides of a parallelogram are and

MATHEMATICS · Single correct · A Level · Mathematics · Vectors · Vectors

Problem

The sides of a parallelogram are

2\hat{i} + 4\hat{j} - 5\hat{k}

and

\hat{i} + 2\hat{j} + 3\hat{k}

. The unit vector parallel to one of the diagonals is (1)

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

(2)

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

(3)

\frac{1}{\sqrt{69}}(\hat{i} + 2\hat{j} + 8\hat{k})

(4)

\frac{1}{\sqrt{69}}(-\hat{i} - 2\hat{j} + 8\hat{k})