Question

If `vec"A"=3hat"i"-2hat"j"+hat"k",vec"B"=hat"i"-3hat"j"+5hat"k" and vec"C"=2hat"i"+hat"j"-4hat"k"` form a right angled triangle then out of the following which one is satisfied?

Options

• `vec"A"=vec"B"+vec"C"` and A² = B² + C²

• `vec"A"=vec"B"+vec"C"` and B² = A² + C²

• `vec"B"=vec"A"+vec"C"` and B² = A² + C²

• `vec"B"=vec"A"+vec"C"` and A² = B² + C²

Answer 1

`bb(vec"B"=vec"A"+vec"C")` and B² = A² + C²

Explanation:

Here, |A| = `sqrt(9+4+1)=sqrt14`

|B| = `sqrt(1+9+25)=sqrt35`

|C| = `sqrt(4+1+16)` = `sqrt21`

Clearly, `vec"B"=vec"A"+vec"C"` and B² = A² + C²