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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→.
If r→ = 3î − 2ĵ + 6k̂, find the value of (r→ × ĵ) · (r→ × k̂) − 12.
If a⃗, b⃗, c⃗ and d⃗ are four non-zero vectors such that a⃗ × b⃗ = c⃗ × d⃗ and a⃗ × c⃗ = 4b⃗ × d⃗, then show that (a⃗ − 2d⃗) is parallel to (2b⃗ − c⃗) where a⃗ ≠ 2d⃗, c⃗ ≠ 2b⃗.
The two adjacent sides of a parallelogram are represented by 2î − 4ĵ − 5k̂ and 2î + 2ĵ + 3k̂. Find the unit vectors parallel to its diagonals. Using the diagonal vectors, find the area of the parallelogram also.
ABCD is a parallelogram such that AC = î + ĵ and BD = 2î + ĵ + k̂. Find AB and AD. Also, find the area of the parallelogram ABCD.
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