The vector projection of b ˉ on, a ˉ = 3 i ^ + 2 j ^ + 5 k ^ and b ˉ = 7 i ^ − 5 j ^ − k ^

The vector projection of b on a = ( ∣ a ∣ b ⋅ a ) a ^ = ( ∣ a ∣ 2 b ⋅ a ) a = ( 3 2 + 2 2 + 5 2 7 × 3 + ( − 5 ) × 2 + ( − 1 ) × 5 ) ( 3 i ^ + 2 j ^ + 5 k ^ ) = 38 6 ( 3 i ^ + 2 j ^ + 5 k ^ ) = 19 3 ( 3 i ^ + 2 j ^ + 5 k ^ )

Mathematics - 3D Coordinate Geometry Question with Solution | TestHub

Mathematics3D Coordinate GeometryCoordinates of a point in space, Direction cosines,Medium2 minPYQ_2022

MathematicsMediumsingle choice

The vector projection of $\overset{ˉ}{b}$ on, $\overset{a}{ˉ} = 3 \hat{i} + 2 \hat{j} + 5 \hat{k}$ and $\overset{ˉ}{b} = 7 \hat{i} - 5 \hat{j} - \hat{k}$

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Answer:

Solution:

The vector projection of $b$ on $a$ $= (\frac{b \cdot a}{∣ a ∣}) \overset{a}{^} = (\frac{b \cdot a}{∣ a ∣ ^{2}}) a = (\frac{7 \times 3 + ( - 5 ) \times 2 + ( - 1 ) \times 5}{3 ^{2} + 2 ^{2} + 5 ^{2}}) (3 \hat{i} + 2 \hat{j} + 5 \hat{k}) = \frac{6}{38} (3 \hat{i} + 2 \hat{j} + 5 \hat{k}) = \frac{3}{19} (3 \hat{i} + 2 \hat{j} + 5 \hat{k})$

Stream:MHT_CETSubject:MathematicsTopic:3D Coordinate GeometrySubtopic:Coordinates of a point in space, Direction cosines,

⏱ 2mℹ️ Source: PYQ_2022

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