Find the coordinates of the foot of the perpendicular drawn from the point P(0, 2, 3) to the line (x + 3)/5 = (y − 1)/2 = (z + 4)/3.

Question

TextScalar Product of Two VectorsCartesian Equation of a Line in Three DimensionsCBSE PYQ

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Let θ be the angle between two unit vectors â and b̂ such that sin θ = 3/5. Then, â . b̂ is equal to :

If a⃗ and b⃗ are two non-zero vectors such that (a⃗ + b⃗) ⊥ a⃗ and (2a⃗ + b⃗) ⊥ b⃗, then prove that |b⃗| = √2 |a⃗|.

Scalar Product of Two Vectors

Properties of Scalar (Dot) Product

The image of point P(x, y, z) with respect to line x/1 = (y – 1)/2 = (z – 2)/3 is P′ (1, 0, 7). Find the coordinates of point P.

For any two vectors a→ and b→, which of the following statements is always true ?

Direction ratios of a vector parallel to line (x–1)/2 = – y = (2z+1)/6 are :

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→.