Let α → = 3 i ^ + j ^ and β → = 2 i ^ - j ^ + 3 k ^ . If β → = β 1 → - β 2 → , where β 1 → is parallel to α → and β 2 → is perpendicular to α → , then β 1 → × β 2 → is equal to:

Step-by-step solution

If two vectors are parallel then they are proportional. So, let β 1 → = k α → Given β → = β 1 → - β 2 → ⇒ α → ⋅ β → = α → ⋅ β 1 → - α → ⋅ β 2 →       . . . i Now, α → · β → = 3 i ^ + j ^ · 2 i ^ - j ^ + 3 k ^ = 6 - 1 = 5 And, α → is perpendicular to β 1 → , hence α → ⋅ β 1 → =