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The vector with terminal point A (2, – 3, 5) and initial point B (3, – 4, 7) is :
The position vectors of vertices of △ ABC are A(2î – ĵ + k̂), B(î – 3ĵ – 5k̂) and C(3î – 4ĵ – 4k̂). Find all the angles of △ ABC.
Assertion (A) : The vectors a⃗ = 6î + 2ĵ − 8k̂, b⃗ = 10î − 2ĵ − 6k̂ and c⃗ = 4î − 4ĵ + 2k̂ represent the sides of a right angled triangle. Reason (R) : Three non-zero vectors of which none of two are collinear forms a triangle if their resultant is zero vector or sum of any two vectors is equal to the third.
If a = î + ĵ − 2k̂, b = −î + 2ĵ + 2k̂ and c = −î + 2ĵ − k̂ are three vectors, then find a vector perpendicular to both the vectors (a + b) and (b − c).
The vectors a = 2î – 4ĵ + λk̂ and b = 3î – 6ĵ + k̂ are collinear if value of λ is :
In △ABC, AB = î + ĵ + 2k̂ and AC = 3î – ĵ + 4k̂. If D is mid-point of BC, then vector AD is equal to :
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