7
To find the resultant vector when multiplying the vector components (3, -3, -2) by the scalar -6, we perform the scalar multiplication: (-6)(3, -3, -2) = (-18, 18, 12). The magnitude can be calculated using the formula ( \sqrt{(-18)^2 + (18)^2 + (12)^2} ), which equals ( \sqrt{1080} ) or approximately 32.8. The direction of the resultant vector is opposite to the original vector due to the negative scalar, meaning it points in the direction of the vector (-3, 3, 2).
7
3 times the magnitude of the vector V - which is not known.3 times the magnitude of the vector V - which is not known.3 times the magnitude of the vector V - which is not known.3 times the magnitude of the vector V - which is not known.
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Vectors are added graphically tip to tail. You subtract vector B from vector A by adding vector -B to vector A. Where -B means a vector that points in the opposite direction as B , but has same magnitude. For example to subtract B (magnitude 4, points left) from vector A (magnitude 3, points up), first draw A, then draw -B (magnitude 4, points right) ,starting -B at the tip of A. Then the vector that connects the tail of A to the tip of -B is the difference A - B or A + (-B) . In this example A & -B form the legs 3 & 4 of a right triangle so the hypotenuse (which is A - B) is 5.
7
5
It is not possible to obtain a vector with a magnitude of 7 when adding vectors of magnitude 3 and 4. The resultant magnitude will be between 1 and 7, as the triangle inequality states that the magnitude of the sum of two vectors is less than or equal to the sum of their magnitudes.
To find the resultant vector when multiplying the vector components (3, -3, -2) by the scalar -6, we perform the scalar multiplication: (-6)(3, -3, -2) = (-18, 18, 12). The magnitude can be calculated using the formula ( \sqrt{(-18)^2 + (18)^2 + (12)^2} ), which equals ( \sqrt{1080} ) or approximately 32.8. The direction of the resultant vector is opposite to the original vector due to the negative scalar, meaning it points in the direction of the vector (-3, 3, 2).
7
3 times the magnitude of the vector V - which is not known.3 times the magnitude of the vector V - which is not known.3 times the magnitude of the vector V - which is not known.3 times the magnitude of the vector V - which is not known.
If the two vectors are in the form: P = ai + bj, and Q = ci + djThen the resultant vector is (a + c)i + (b + d)jand the magnitude is:sqrt((a +c)2 + (b + d)2)If 3 dimensional, then the k components are added then squared and added to the i & j components, before taking the square root.
Polygon Method Of Adding Vector1. Draw the first vector using a scale.2. Connect the tail, the 2nd vector to the arrow head to first vector. Repeat desame procedures with the other vector.3. Join the tail of the first vector to the arrow head of the last vector to determine the magnitude and direction of resultant.4. The length of resultant draw the scale determines the magnitude and the direction is the angle between the arrow head of the last vector.
The multiplicative resultant is a three unit vector composed of a vector parallel to the 3 unit vector and a vector parallel to the product of the 3 unit and 4 unit vectors. R = (w4 + v4)(0 +v3) = (w40 - v4.v3) + (w4v3 + 0v4 + v4xv3) R = (0 - 0) + w4v3 + v4xv3 as v4.v3 =0 ( right angles or perpendicular)
Scalar quantities are added algebraically. But vector quantities are added using vector addition. If 3 and 4 are added only 7 is the result. If two vectors with magnitude 3 and 4 are added there will be different results such as 7, 1, 5, etc etc. 7 will be the answer if both the vectors are in the same direction. 1 will be the answer if both are in opposite direction 5 will be the answer if both act perpendicular to each other. Other innumerable answers are possible as both vectors act with different angles of inclination.
-- A singe vector with a magnitude of zero produces a zero resultant.-- Two vectors with equal magnitudes and opposite directions produce a zero resultant.
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