Question

If `bar"a", bar"b", bar"c"` are the three non-coplanar vectors and `bar"p", bar"q", bar"r"` are defined by the relations `bar"p" = (bar"b" xx bar"c")/([(bar"a", bar"b", bar"c")]), bar"q" = (bar"c" xx bar"a")/([(bar"a", bar"b", bar"c")]), bar"r" = (bar"a" xx bar"b")/([(bar"a", bar"b", bar"c")])` then `(bar"a" + bar"b")* bar"p" + (bar"b" + bar"c") * bar"q" + (bar"c" + bar"a") * bar"r"` = ______.

Options

• 0

• 1

• 2

• 3

Answer 1

If `bar"a", bar"b", bar"c"` are the three non-coplanar vectors and `bar"p", bar"q", bar"r"` are defined by the relations `bar"p" = (bar"b" xx bar"c")/([(bar"a", bar"b", bar"c")]), bar"q" = (bar"c" xx bar"a")/([(bar"a", bar"b", bar"c")]), bar"r" = (bar"a" xx bar"b")/([(bar"a", bar"b", bar"c")])` then `(bar"a" + bar"b")* bar"p" + (bar"b" + bar"c") * bar"q" + (bar"c" + bar"a") * bar"r"` = 3.

Explanation:

`bar"p"*(bar"a" + bar"b") = bar"p"*bar"a" + "p"*bar"b"`

= `((bar"b" xx bar"c")*bar"a")/([(bar"a", bar"b", bar"c")]) + ((bar"b" xx bar"c")*bar"b")/([(bar"a", bar"b", bar"c")])`

= `([(bar"b", bar"c", bar"a")])/([(bar"a", bar"b", bar"c")]) + ([(bar"b", bar"c", bar"b")])/([(bar"a", bar"b", bar"c")])`

= 1 + 0

 1

Similarly, `bar"q"*(bar"b" + bar"c")` = 1 and `bar"r"*(bar"a" + bar"c")` = 1

`(bar"a" + bar"b")*bar"p" + (bar"b" + bar"c")*bar"q" + (bar"c" + bar"a")*bar"r"` = 1 + 1 + 1 = 3