JEE Advanced 2015 · Paper 2 · Mathematics Q48

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MathematicsInteger+4Question 48 of 60

Suppose that $\vec p$ , $\vec q$ and $\vec r$ are three non-coplanar vectors in $\mathbb R^3$ . Let the components of a vector $\vec s$ along $\vec p$ , $\vec q$ and $\vec r$ be 4, 3 and 5, respectively. If the components of this vector $\vec s$ along $(-\vec p+\vec q+\vec r)$ , $(\vec p-\vec q+\vec r)$ and $(-\vec p-\vec q+\vec r)$ are $x$ , $y$ and $z$ , respectively, then the value of $2x+y+z$ is

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Answer and worked solution

Official answer: Bonus: full marks to everyone

Official key: 9, with +4 marks awarded to all candidates.

Match coefficients. Write $\vec s=4\vec p+3\vec q+5\vec r=x(-\vec p+\vec q+\vec r)+y(\vec p-\vec q+\vec r)+z(-\vec p-\vec q+\vec r)$ :
$-x+y-z=4,\qquad x-y-z=3,\qquad x+y+z=5.$

Solve. $z=-\frac72$ , $y=\frac92$ and $x=4$ .

Value. $2x+y+z=8+\frac92-\frac72=9$ .

Answer: 9 (marks to all)

Topics:Scalar and vector triple products Vector operations

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JEE Advanced 2015 · Paper 2, Mathematics question 48