In the given figure, ABCD is a parallelogram. If AB⃗ = 2î – 4ĵ + 5k̂ and DB⃗ = 3î – 6ĵ + 2k̂, then find AD⃗ and hence find the area of parallelogram ABCD.

Question

TextVector Product of Two VectorsGeometrical Interpretation of Vector ProductCBSE PYQ

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The unit vector perpendicular to both vectors î + k̂ and î – k̂ is :

Assertion (A) : For two non-zero vectors a→ and b→, a→ · b→ = b→ · a→. Reason (R) : For two non-zero vectors a→ and b→, a→ × b→ = b→ × a→.

Scalar Product of Two Vectors

Vector Product of Two Vectors

Properties of Scalar (Dot) Product

Properties of Vector (Cross) Product

Let a→ and b→ be two non-zero vectors. Prove that |a→ × b→| ≤ |a→||b→|. State the condition under which equality holds, i.e., |a→ × b→| = |a→||b→|.

Let →a be any vector such that |→a| = a. The value of |→a × î|² + |→a × ĵ|² + |→a × k̂|² is:

Find a vector of magnitude 4 units perpendicular to each of the vectors 2î − ĵ + k̂ and î + ĵ − k̂ and hence verify your answer.

Given a⃗ = 2î - ĵ + k̂, b⃗ = 3î - k̂ and c⃗ = 2î + ĵ - 2k̂. Find a vector d⃗ which is perpendicular to both a⃗ and b⃗ and c⃗ · d⃗ = 3.