Question

If `bar"a"` makes an acute angle with `bar"b", bar"r"*bar"a"`  = 0 and `bar"r"xx bar"b" = bar"c"  xx bar"b"`, then `bar"r"` = ______.

पर्याय

• `bar"a"xx bar"c" - bar"b"`

• `bar"c" xx bar"a"`

• `bar"c" - ((bar"c" * bar"a")/(bar"b" * bar"a"))bar"b"`

• `bar"c" + ((bar"c" * bar"a")/(bar"b" * bar"a"))bar"b"`

Answer 1

If `bar"a"` makes an acute angle with `bar"b", bar"r"*bar"a"`  = 0 and `bar"r"xx bar"b" = bar"c"  xx bar"b"`, then `bar"r"` = `bar"c" - ((bar"c" * bar"a")/(bar"b" * bar"a"))bar"b"`.

Explanation:

`bar"r"xx bar"b" = bar"c"  xx bar"b"`

⇒ `bar"a" xx (bar"r" xx bar"b") = bar"a" xx (bar"c" xx bar"b")`

⇒ `(bar"a"*bar"b")bar"r" - (bar"a"*bar"r")bar"b" = (bar"a"*bar"b")bar"c" - (bar"a"*bar"c")bar"b"`

⇒ `(bar"a"*bar"b")bar"r" - 0 = (bar"a"*bar"b")bar"c" - (bar"a"*bar"c")bar"b"`

⇒ `bar"r" = bar"c" - ((bar"c" * bar"a")/(bar"b" * bar"a"))bar"b"`