(a) Let $\vec{\alpha}, \vec{\beta}, \vec{\gamma}$ be three non-zero vectors, such that $\vec{\alpha} \times \vec{\beta} = \vec{\gamma}$ and $\vec{\beta} \times \vec{\gamma} = \vec{\alpha}$. Show that $\alpha, \beta, \gamma$ are mutually perpendicular vectors such that $|\vec{\beta}| = 1$ and $|\vec{\alpha}| = |\vec{\gamma}|$. Find projection of vector $\vec{\alpha}$ on $\vec{\beta}$. Give reasons to support your answer. OR (b) If points $A(3, -1, 2)$, $B(6, -3, 6)$, $C(4, -3, 1)$ and $D(1, -1, -3)$ are vertices of a quadrilateral $ABCD$, write the position vectors of $A$, $B$, $C$ and $D$ and show that $ABCD$ represents a parallelogram. Also, find the area of the parallelogram $ABCD$.

Year	Paper Code	Set	Position
CBSE 2026	Series 65-7	Set 1	Question 35
CBSE 2026	Series 65-7	Set 2	Question 33
CBSE 2026	Series 65-7	Set 3	Question 35

• Step 1: Stating the fundamental formula / law statement (+1 Mark)
• Step 2: Intermediate mathematical substitution or proof steps (+1 Mark)
• Step 3: Correct final value or conclusion with mandatory SI units (+1 Mark)