The four points A, B, C, D have position vectors pi, j+qk, k, and i+j respectively, where p and q are positive real numbers. Given that AB and CD are perpendicular, express q in terms of p, and show that the angle between AC and BD is equal to the angle between AD and BC.
The four points A, B, C, D have position vectors pi, j+qk, k, and i+j respectively, where p and q are positive real numbers. Given that AB and CD are perpendicular, express q in terms of p, and show that the angle between AC and BD is equal to the angle between AD and BC.
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The four points A, B, C, D have position vectors pi, j+qk, k, and i+j respectively, where p and q are positive real numbers. Given that AB and CD are perpendicular, express q in terms of p, and show that the angle between AC and BD is equal to the angle between AD and BC.
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